# which three statements are true? a) if x= -10^4 then log 10 = -4 b)if x= 2^8 then log 2x = 8 c) log2 2= 4 d) if x= 3 then log10 3=x e) log 10 256-2log 10 a/log 10

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### mathematics -logs

which three statements are true? a) if x= -10^4 then log 10 = -4 b)if x= 2^8 then log 2x = 8 c) log2 2= 4 d) if x= 3 then log10 3=x e) log 10 256-2log 10 a/log 10 b f)log 10 (a-b)= log 10 a/log 10 b g) the gradient of the graph of y= 2x^x at x= 2 is 2e^e h) the gradient of the...

### math

Logarithm!!! Select all of the following that are true statements: (a) log(2x) = log(2) + log(x) (b) log(3x) = 3 log(x) (c) log(12y) = 2 log(2) + log(3y) (d) log(5y) = log(20y) – log(4) (e) log(x) = log(5x) – log(5) (f) ln(25) = 2ln(5) (g) ln(1) = log(1) (h) ln(e) = log(10...

### maths

which three statements are true? a) if x= -10^4 then log 10 = -4 b)if x= 2^8 then log 2x = 8 c) log2 2= 4 d) if x= 3 then log10 3=x e) log 10 256-2log 10 a/log 10 b f)log 10 (a-b)= log 10 a/log 10 b g) the gradient of the graph of y= 2x^x at x= 2 is 2e^e h) the gradient of the...

### maths

which three statements are true? a) if x= -10^4 then log 10 = -4 b)if x= 2^8 then log 2x = 8 c) log2 2= 4 d) if x= 3 then log10 3=x e) log 10 256-2log 10 a/log 10 b f)log 10 (a-b)= log 10 a/log 10 b g) the gradient of the graph of y= 2x^x at x= 2 is 2e^e h) the gradient of the...

### math

which three statements are true? a) if x= -10^4 then log 10 = -4 b)if x= 2^8 then log 2x = 8 c) log2 2= 4 d) if x= 3 then log10 3=x e) log 10 256-2log 10 a/log 10 b f)log 10 (a-b)= log 10 a/log 10 b g) the gradient of the graph of y= 2x^x at x= 2 is 2e^e h) the gradient of the...

### Math

1. The sequence log2 32, log2 y, log2 128, ... forms an arithmetic sequence. What is the value of y? 2. If log a^2 b^3 = x and log (a/b) = y, what are the values of log a and log b?

### precalc

I don't understand how to do these w/o calc. I tried to write it in a way that will make someone understand how to read it. Hope I typed it clear enough.Thanks so much for the help anyone! How to find the exact value of logarithm: 10. log5^100 -log5^4 11. log4^8 +log4^8 12. ...

### Math

Are all statements that are true. (a) log(A)/log(B)=In(A)/In(B) (b) In log[b](N), the exponent is N. (c)If 2log[3](81)=8, then log[3](6.561)=8 (d)log[b](N) negative when N is negative. (e)In(x/2)=In(x)/2

### Math

Are all statements that are true. (a) log(A)/log(B)=In(A)/In(B) (b) In log[b](N), the exponent is N. (c)If 2log[3](81)=8, then log[3](6.561)=8 (d)log[b](N) negative when N is negative. (e)In(x/2)=In(x)/2

### math

write as a single logarithm: -2logbase3(1/x)+(1/3)logbase3(square root of x) please show the steps to solving this. thanx. remember that 1 log (AxB) = log A + Log B (same base) 2 log (A/B) = log A - log B 3 log A^n = n log A use these three rules and it becomes an easy question.

### Math Help Please

Which of the following expressions is equal to log (x sqrt-y)/z^5 A. log x + log (1/2) + log y– log 5 – log z B. log [x + (1/2)y – 5z] C. log x + (1/2)log y – 5 log z d. [(1/2) log x log y]/(5 log z)

### Math

The problem I have to solve is log with base 2 ^6 multiply by log base 6 ^ 8. I use the change of base formula and got log6/log2 * log8/log6 Which become log6/log2 * log2()^3/ log 6 I'm stuck here thanks.

### Mathematics

Prove that log a, log ar, log ar^2 is an a.p. Is the following below correct? Log ar^2 - Log ar= Log ar - Log a hence applying laws of logarithm Log(ar^2/ar) = log(ar/a) Log and log cancels out and then cross-multiply hence a^2r^2 = a^2r^2 L.H.S=R.H.S Hence proved?

### Logarithms

I'm working on logarithmic equations and I'm stuck on how my book arrives at the next step. First, they use the change of base formula on, log(sqrt(2))(x^3 - 2) (sqrt(2)) is the base,changing to base 2 log(sqrt(2))(x^3 - 2)= log2(x^3 - 2)/(log2(sqrt(2)) I understand that part...

### maths

1. Log10²x+log10x²=log10² 2-1 2. Log4(log2x)+log2(log4x)=2 3. X^logx+5/3= 10^5+log x 4. Log 1/2(x-1)+ log 1/2(x+1)-log1/√2(7-x)=1

### Algebra 2

how do not understand how to do this Log X + Lob (X-3) = 1 I know I do this Log X(X-3)=1 then I do this Log X^(2) - 3X = 1 then I do this 2 Log (X-3X) = 1 then 2 Log (-2X) = 1 then (2 Log (-2X) = 1)(1/2) Log (-2X) = 1/2 then (Log (-2X) = 1/2)(-1/2) Log X = (-1/4) then by def ...

### calc

given that log2 3 = x, log 2 5=y and log 2 7 = z, express log 2 21 in terms of x,y, and z the 2 is the base

### math(Please help)

1) use the properties of logarithms to simplify the logarithmic expression. log base 10 (9/300) log - log 300 log 9 = 2 log 3 log 300 = log 3 + log 100 = log 3+2 I just do not know how to put these together now!

### math

which 3 are correct a) if x= -10^4 then log10 x = -4 b)if x= 2^8 then log 2x = 8 c) log2 2= 4 d) if x= 3 then log10 3=x e) log 10 256-2log 10 16=0 f)log 10 (a-b)= log 10 a/log 10 b g) the gradient of the graph of y= 2e^x at x= 2 is 2e^2 h) the gradient of the graph of y= e^x ...

### Precaculculus

Suppose you are told that log(2)=0.3562 and log(3)=0.5646. All of them with the base of 'a'. Find: i) log(6) ii) log(9) Solutions i) log(6)= log (3)(2) = log 3 + log 2 = 0.5646 + 0.3562 = 0.9208 ii)log(9)= log 3^2 = 2 log 3 = 2 (0.5646) = 1.1292

### Trigonometry

This is a logs question If u=x/y^2, which expression is equivalent to log u? 1) log x + 2 log y 2) 2(log x- log y) 3) 2(log x + log y) 4) log x- 2 log y

### Math/trig

Log radical b/ a^2 is equivalent to 1) 1/2 log b + 1/2 log a 2) l/2 log b- 2 log a 3) 2 log b - 1/2 log a 4) 1/2logb/2 log a

### precalc

Suppose that u=log(2) and v=log(5). Find possible formulas for the following expressions in terms of u and/or v. Your answers should NOT involve any log's. a) log(0.4)= b) log(0.08)= c) log(2500)=

### college algebra

Write expression as one logarithm and simplify if appropriate. log 3√x + log x^4 - log x^3 4 log (x+3) - 5 log (x^2+4) + 1/3 log y I have these who problems but I don't know where to start. HELP Please.

### Calculus AB

How do you solve a system of logarithmic equations? They have completely different bases: {(log(25)^3)x + (log(2)^7)y = log(5)^27 {(log(7)^8)x + (log(3)^5)y = log(49)^2

### Trigonometry

The expression log(x^n/ radical y)is equivalent to 1. n log x - 1/2 log y 2. n log x- 2 log y 3. log (nx) - log (1/2y) 4. log (nx) - log (2y)

### Algebra 2

-Explain the difference between log base b (mn) and ( log base b of m)(log base b of n). Are they equivalent? My answer: Let b=2, m=8, n=16 *log base b (mn)=log base b of m + log base b of n log base 2 of 8+ log base 2 of 16=7 * (log base b of m) (log base b of n)=(log base 2 ...

### Advanced Functions/ Precalculus Log

1. Evaluate 4^(log base4 64) + 10^(log100) 2. Write 1+log(base2)x^3 as a single logarithm 3. Write log(base b)√(x^3 y z^6) 4. Solve log(base 2)x-log(base 2)6=log(base 2)5+2log(base 2)3 5. Solve 3^(2x) = 9(81^x) 6. Solve 3^(2x)=7^(3x-1). Round answer to two decimal places...

### precalc(LOGS) CONFUSED!

How do I rewrite without logarithms?? 2. log x= log a - 4 log b 3. ln t= 3/2 ln a - ln p 4. log y = 3 log x + log 17

### Trigonometry

Every point (x,y) on the curve y=log(3x)/log2 is transferred to a new point by the following translation (x′,y′)=(x−m,y−n), where m and n are integers. The set of (x′,y′) form the curve y=log(12x−96)/log2. What is the value of m+n? ...

### TRig WIth LoGs help1!!

i have problem i can't solve and the book is no help.. anyone got osme hints or somehting i could start off doing? the problem is... Solve for x: log(x^3)= (log x)^3 Rewrite it as 3 log x = (log x)^3 The use algebra (divide each side by log x) to get (log x)^2 = 3 log x = (+ ...

### MATH

Write as a single logarithm: 2 log 3 – log 5 +2 log2

### Math

solve log(7x-3)+2log(5)=2+log(x+3) I've attempted to do this question and I ended up with log(7-3)+log(5^2)-log(x+3)=2 but I don't what to do next or whether I did something wrong.

### Algebra 2

How is the expression log 32 - log 8 written as a single logarithm? log 4 log 8 log 24 log 40

### mathematics

given that log(6)/log(a) = p and log(108)/log(a) = q , express log(3)/log(a) in terms of p and q

### math

write as a single logarithm: ln(x/x-1)+ ln(x+1/x)- ln(x^2-1) please show me the steps. thanx Michelle, I hope you know the three main rules of logs. 1. log (AB) = log A + log B 2. log (A/B) = log A - log B 3 log A^n - n log A Using these rules and guessing at your order of ...

### precalculus

solve log(2+x)-log(x-3)=log2 I know the answer is 8

### Algebra-Please check

Write y = 10^(x) as a logarithmic function Choices are log(x)10 = y log(y)x = 10 log(10)y = x log(x)y = 10 I think it is log (10)y = x

### chemistry

The definition of pH is: pH = -log 10[H^+] what is the defintion of the [OH^-]... is it pOH = -log 10[OH^-]? Yes!! pH = - log10 anything. pKa = -log Ka Pkb = -log Kb pKw = -log Kw = 14 PKsp = -log Ksp (solubility product) and so on into the night.

### math

state the values of x for which the following identiy is true log(x+2) + log(x+3) = log(x^2+5x+6) a) x> -2 b) x> -3 Why is the answer a and not b? If it was b, then it would include -2

### MATH

true or false: log (x-y) = log (x) - log(y) I don't know the the first part, but looking at the second part, wouldn't log (x) - log (y) = log x/y so based on that the first part is false?

### Math

How would you solve this equation? log(ab)=log(a)*log(b) a=30, b=60 Does the it appear that this is a true statement? Why?

### Pre-Cal

log 3x=log2+log(x+5)

### math

solve log(2+x)-log(x-3)=log2

### more math

Are the following statements true ? log(-3) + log(-4) = log12 -log3 - log4 = -log12 Explain why or why not

### more math

Are the following statements true ? log(-3) + log(-4) = log12 -log3 - log4 = -log12 Explain why or why not

### math

Given: f(x)=log 5 x what is the value of f(125) and f(1/25)? Totally lost! I assume you mean f(x) = log (5x), not log 5 * x. If this is the case, then f(125) = log 600 and f(1/25) = log (1/5) If the base of the logs is 10, then log 600 = 2.778..

### math

Q1:solve log(5)x-log(25)(x+10) = 0.5 Q2:If 2log(a)x=1+log(a) (7x-10a) ,find x in terms of a. Q3:Find x for which 27x3^lgx = 9^1+lg(x-20) Q4:Find x in terms of a and c ,given that log(√ a)(1/x)+log(a)x +log(a^2) x +log (a^4)x=c

### Math

h(x) = log (6x+5/7x-4) Find a formula for the inverse function h^-1(x) h^-1(x) = My work so far h(x) = log(6x+5/7x-4) y=log(6x+5/7x-4) x=log(6y+5/7y-4) 7xy-4x= log(6y+5) how would I solve from here. Would I solve for y then do the natural log of both sides or do the natural ...

### Math

The problem 8^x = 16^x+2 the choices a)8 and b)-8. Help please! Given that information I want to say the answer is -8 ? where is the 2. Use parentheses. Is it 16x+2 or 16x+2 The 2 is part of the exponent. Take the log of both sides. log 8x=log 16x+2 x*log 8 = x+2*log 16 solve ...

### Chemistry/Algebra 2

Are the answers to these correct? Use log(base12)3= 0.4421 and log(base12)7= 0.7831. log(base12)36 = log(base12)3^2*4= 4.8842 log(base12)27/49 = -0.2399 log(base12)81/49 = 0.2022 log(base12)16,807 = 3.9155 (16,807= 7^5) log(base12)441 = 2.4504 (441= 7^2*3^2)

### math30

1.Use the laws of logarithms to express log2 (6) â€“ log2 (3) + 2log2 (8)^1/2 as a single logarithm; then evaluate. 2. For logy = log(0.5x â€“ 3) + log2, express y as a function of x.

### math

mathematically Evaluate without using tables 2 log base 10 raised 2 power 5 + log base 10 36 - log base10 9 that is, 2log10 5 +log 10 36 - log 10 9

### math

solve for x without using a calculator 5^(x+1) = 25 i know that x would equal 1 because 5^2 is 25, but i don't know how to show how to solve it All you need to do is what you just did: Explain that if x = 1, the equation is satisfied. If you are looking for a method of ...

### Math PLEASE HELP!

I am really struggling with these questions. Any help is appreciated. Approximate x to three decimal places. log x = 3.5829 log x = 0.6703 log x = −1.5959

### Precalculus

PLEASE HELP ME WITH THESE QUESTION AS MUCH AS POSSIBLE!! Evaluate without a calculator. Give exact answers: a) log(log(10)) = ? b) square root (log(100)) - log(square root(100)) = ? c) log((square root 10^3)(square root 10^5)(square root 10) = ? d) 1000^log(3) = ? e) log(1/log...

### algebra

logarithms Solve the following equations 3^x-2=6 Add 2 to both sides of the equation to start. Whatever operation you do to one side of an equation you must do to the other side as well. 3^x - 2 + 2 = 6 + 2 3^x = 8 Changing to logs: log 3^x = log 8 x log 3 = log 8 x = log 8 / ...

### Math - Logarithmic

Solve: 2^(5x-6) = 7 My work: log^(5x-6) = log7 5x - 6(log2) = log7 5x = log7 + 6(log2) x = (log7 + log2^6) / 5 And textbook answer: (log7) / (log2) What did I do wrong?

### Algebra-Please check

y= 6x is written as: Choices y = log(6)x x = log(6)y I chose y = log(6)x, correct?I did the inverse so x = 6^x isolate y so it becomes y = log(6)x

### Algebra-Please check my answer

y= 6x is written as: Choices y = log(6)x x = log(6)y I chose y = log(6)x, correct?I did the inverse so x = 6^x isolate y so it becomes y = log(6)x

### math

Calculate without using tables or calculators log 450 and log 324 given log 2 =0.3010 and log 3 =0.4771

### Math-LOGS

Express x in terms of a,b and c. log x = 1/2 (log a + log b - log c) Please solve and explain how to do this type of problem, thank you!

### maths

Combine into one log: log √ x + 1 + 9 log x i.e. rewrite as an expression of the form log u, where u is a function of x.

### Re: Algebra II

How to solve Log (9x+5) - Log ((x^2)-1) = 1/2 16 16 (The 16 is from the logarithmic function : b) (y=log x) b Could anyone post the answer to this? 16 is supposed to be next to Log(16) but lower. This is for both the Logs in the equation.

### calculus

Use a linear approximation of f(x)=log(x) at x=1 to approximate log(3/4). Express your answer as an exact fraction; remember that log denotes the natural log.

### Algebra please can you ck my work

Evaluate the given expressions (to two decimal places). log 1.69 =123 log 2^512 = .09 log 2^1 = 0 log o.o46 =1.34 Thank you

### Trig

log base b 64 - log base b 16 = log base 4 16 solve for the variable.. i got to the part as far as: (log 4/log b) = 2 now i m stuck at how i can isolate the b. plz help!

### Chemistry

True or false question The pH of 0.1mol/L acetic acid is 1. So the amswer is False, the pH is greater than 1. How is pH-log(0.1)=1 wrong? I researched and found this solution but I don't know why I cant use pH=-log ([H+]) Ka=1.8×10^-5 1.8=x^2÷x I get x=1.34 x 10^-3 pH=-log (...

### Precalculus

More log/exponential equations log2 x + log2(x+2) =3

### precalc

If g(x = log subscript 7 x then what is the value of g(1/49)? I believe it's 1/2 but I'm not sure. no recall that log 1/49 (base7) = log 1 - log 49 = 0 - 2 =-2

### math -- log and exp. functions

1. evaluate log(base2)[(1/32) X 4^-9] 2. simplify: log x^2 y - (1/2)logx + 3 log y

### Algebra

How would I write 1-2log(7)x as a single logarithm Choices: log(7) x^2/7 log(7) 7x^2 log(7) 7/x^2 log (7) x^2 Thank you

### maths pls help

1. Solve the following simultaneous equations: log2 xy = 7 log2 (x^2/y) = 5 2. If log y x =a and log z x=b where x is not equal to 1, express the following in terms of a and b: logy (yz) Solve the following simultaneous equations: y = 2 log3 x y+1 = log3 9x Thanks! I tried to ...

### Further mathematics

Given that x squared + y squared = 5xy,show that; (a) 2log(x+y\√7)=log x + log y. (b). Log ( x- y\√3) = 1\2( log x + log y)

### Algebra II

Please check answers: Use the equation of the exponential function whose graph passes through the points (0,-2) and (2,-50) to find the value of y when x= -2. My answer: -2/25 Solve 64^x<32^x+2 Answer: x<10 Write the equation log(243)81=4/5 Answer: 243^4/5 = 81 Evaluate ...

### pre-calculus

What is the base of the function F(x) = b to the power of x if the graph has points of (1/3, 2)and another off the subject one if g(x)= log 7 x what is g(1/49)? If F(x) = 2 when x = 1/3, and if the fucntio is of the form F(x) = b^x, then 2 = b^(1/3) Cube both sides of the ...

### Math

prove: 1/log(base36)a = 2/log(base6)a i made a common base and then multiplied both sides with log(base6)a to get 2=log(base6)a/log(base6^2)a but this is as far as i can figure.

### Logarithms

Hi, Can anyone tell me if the following are correct please:- If x = 10y (where x > 0), then log10 x = y if a and b are positive numbers, then, 2 log 10 a / b = 2log 10 a - 2 log 10 b and lastly if a and b are positive numbers, then, log 10 ( a+b ) = 10 log 10 a + log 10 b ...

### Calculus

Integrate x dx/(1-x). I have proceeded thus- Int xdx/(1-x)=int -(x-1+1)/(x-1) =-Int[1+ 1/(x-1)]dx =-Int dx-Int dx/(x-1) =-x-log(x-1). On differentiating, we get original expression- d/dx[-x-log(x-1)]=-1-1/(x-1)=-x/(x-1)=x/(1-x). However, the answer in the book is -x-log(1-x)...

### trigonometry

This is an outline that i have to use to find the solution of the question. It involves logarithms and half-angle formulas.I have worked though it but got stuck on some parts. I'd like if you look over my work. solve the triangle for which given parts are a=27 ,b=21 ,c=24 Now ...

### precalc

Solve: round to the thousandths if necessary! 1) 4^3/4x+5 = 12 2) log(x-1) + log x = log 6 3) 2log(base 4) 5 - log(base 4) x + log(base 4) 3 - log(base 4) 7 = 1/2

### check!

here is the question: log5(x-4)= log7x solve for x. These are just base 10 logs. log100 = 2 This equation has the same format as log 40 = log (2x20) Since both sides have log base 10, you divide by log base 10 and end up with 5(x-4) = 7x, so 5x -20 =7x x=-10 One doesn't ...

### algebra/please can you ck my answers

Tell what the output value is for the function machine for the given values. log 16.9=1.23 log2^152=9 log2^1=0 log0.046=1.34 thank you

### 11th grade-Logs

log x = 1/2 (log a + Log b - log c) express x in terms of a,b,and c.

### algebra homework

please check my answers. Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. ln sqrt x+6 = 9 i got {e^9-6} log (x + 4) = log (5x - 5) i got: 9/4 log (x + 30) - log 2 = log (3x + 2...

### Calculus

Find the inverse of each relation: y = (0.5)^(x+2) and y = 3log base 2 (x-3) + 2 For the first one I got y=log base 0.5 (x+2)...but the answer in the back of the textbook says that it is not x+2, but x-2. Can someone tell me why it would end up being x-2 and help me with the ...

### Algebra 2 once more

I have more answers that I would like checked. Also, there is one that I'm really confused about. I appreciate any help. :) Rewrite as the log of a single number. 1) 8 ln 2 = ln(2^8) 2) log 42 - log 6 = log 36 (I think this one may be wrong). Evalute each expression w/o a ...

### Math

What is log x + log x + log x = 3? I want to say 3000 since 10^3=1000, then three times makes 3000.

### Trigonometry /Logarithms (brace yourself)

This is an outline that i have to use to find the solution of the question. It involves logarithms and half-angle formulas.I have worked though it but got stuck on some parts. I'd like if you look over my work. solve the triangle for which given parts are a=27 ,b=21 ,c=24 Now ...

### maths

Let's denote the three numbers by a1, a2, and a3. Consider the third degree polynomial: p(x) = (1 + a1 x)(1 + a2 x)(1 + a3 x) Take the logarithm: Log[p(x)] = Log(1 + a1 x) + Log(1 + a2 x) + Log(1 + a3 x) Expand in powers of x by using that: Log(1 + x) = x - x^2/2 +x^3/3 - x^4/...

### Math: Algebra2 Logarithms

Can someone help me find the value of B in this expression???? log 64 = Blog 4 5 5 Grrr... sorry about that. Here's the expression again: log (base = 5) 64 =B log (base = 5) 4 log 64 (base5) = log 4^b (base5) so 64 = 4^b by recognition of 64 as a power of 4, b=3

### Logarithm help

using logarithms to solve exponential equations. 5^1+x = 2^1-x I need exact numbers. I did one on my own already. 5^x-1 = 9 5^x-1 = 9 log(5^x-1) = log9 (log5)(x-1) = log9 x-1 = (log9/log5) x= (log9/log5)-1 x = 2.3652 Logarithm help - Joe, Friday, September 18, 2015 at 10:55pm ...

### chemistry

Please, can someone help? Evaluate log 1. This is my work up until I have gotten stuck: log 1 1=10^x I can't find a common base for 1 and 10^x. Wow, my apologies, this is algebra, not chemistry. but actually I think they use it in chemistry too... Take the log base 10 of each ...

### Math

Find the exact solution, using common logarithms, and a two-decimal-place approximation of each solution. log(7x + 4) = 2 + log(2x − 3) Solve the equation. log(x^3) = (log x)^2

### Math

Help with these problems would be greatly appreciated: 1.Find the definite integral of dx/(x(1+ln(x))from e^6 to 1. 2. Solve for x in terms of k for log[2,x^6)+log[2,x^10=k. (its log base 2) 3.Solve log base 3(log base 3, x)=-2

### math

1)given that log(y)/log(4)=a and log(2y)/log(8)=b, show that 2a=3b-1 2)the strength (S) of an earthquake is represented by ritcher scale (R) and the relationship is as follows: R=log(S)/log(10).show that when the ritcher scale shows an increase in value by 1,the strength of ...

### Inequality prob#2

log(x-2) + log(9-x) < 1 log(x-2) + log(9-x) < 1 log(x-2)(9-x)<1 (x-2)(9-x)<10^1 and solve.

### Logarithms

How is log(a/bc) the same as log(a) - log(b) - log(c). Should it not be '+ log (c)'?

### Physics

A cylindrical log of uniform density and radius 20.0 cm floats so that the vertical distance from the water line to the top of the log is 8.00 cm. What is the density of the log? (Hint: draw a good picture of the circular end of the log.)