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
50,142 results
Logarithms
CONDENSE INTO THE LOG OF A SINGLE QUANTITY: (1) Base 7 2/3 log( z  2 ) (2) 2 ln8 + 5 ln( z  4 ) (3) Base 4 1/2 [ log( x + 1 ) + 2 log( x  1 ) ] + 6 logx

math
Given that 2 log base2 (x+15)  log base2 x = 6 1.Show that x^2 34x +225 = 0 2. Hence or otherwise solve the equation 2 log base 2 (x+15)  log base 2 x =6

Biochemistry
Calculate how you would make 0.5L of a 0.5M (500mM) acetate buffer at a pH of 4.7. Available is sodium acetate and glacial acetic acid. pH=4.7 pKa of acetic acid=4.76 Not sure if I did this next part right: 4.7=4.76 + log [base]/[acid] 0.06= log

math
If log (base b) 3 = 1.099 and log (base b) 6 = 1.792, find log (base b) 18 = ???

Algebra 2
Condense the expressions 1) 10 log x + 2 log 10 2) 1og base 5 of 8  log base 5 of 12 Can you please explain to me how do you condense these expressions? Thanks in advanced!

chemistry
Q: Calculate the pH of a solution that is 0.56 M HC3H5O3 and 1.28 M NaC3H5O3. I used the HH equation for this and got this so far: HC3H5O3 acid NaC3H5O3 base pH = pKa + log([NaC3H5O3]/[HC3H5O3]) = log(Ka of HC3H5O3) + log(1.28/0.56) = log(1.4*10^4) +

Econ math/logarithms
If log with base b (2)=0.39 and log with base b (3)=0.61 evaluate the following. log with base b (8). Simplify your answer. How to start? I thought I am supposed to write log base b 2^3 but I don't seem to get an answer that would fit.

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!

Algebra 2
Express as a single logarithm. 1/2 log base b of (x2) log base b of y + (3 log base b of z) = log base 6 of (x2)^1/2

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.

Algebra 2
Use the laws of logarithms to condense the following expressions. log base 5 of 6  log base 5 of x

algebra
Find value of log (base 8)log (base 2) log (base 3)log (base 3) (27)^3 I endedup with 1.000063462 which was wrong

pre calculous
use the properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. show your work ln x^2/y^3 Assuming x,y AND z are positive use properties of logariths to write the expression as a single logarithm

interesting log problem
log base 2n 1944 = log base n (486* (2)^1/2) find n^6

math
solve the simultaneous equations; log x base 2log y base 4=4, log (x2y)base 2=5

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

College Algebra
Solve the logarithmic equation. Express your solutions in exact form only. Please show all of your work. log base 6 (64x^3+1)log base 6 (4x+1)=1

log graph
How do you graph y= log (base 5)(x)? The written question is: Sketch above equation by first describing the transformations performed on the equation y= log (base 5)(x) And what is the inverse function? x=log (base 5)(y)?

Logarithms
Prove that log base a of x divided by log base a/b of x is equal to 1+log base a of(1/b) Where do I start?

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!

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
given log 2 base 7 is 0,3562 and log 3 base 7 is 0,5646 evaluate log 42 base 7 without using calculator or tables

Precalculus
Verify these answers please. 1. Which of the following functions would f(x) = log(base 10)x horizontally 4 units to the left? a) f(x)=log(base10)(x4) b) f(x)=4Log(base10)X c) f(x)=log(base10) x+4 Answer: C  2. State the

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

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) =

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

Algebra 2
Explain the difference between log base b of m plus log base b of n and log base b (m+n). Are they equivalent? Explain the difference between log base b (mn) and ( log base b of m)(log base b of n). Are they equivalent?

maths
Solve this logarithmic equation. 3 log 2 base x + log 18 base x = 2

Math
So I have a question regarding advanced functions, logarithm stuff. here is the question: Beginning with the function f(x) = log[base(a)]x ,state what transformations were used on this to obtain the functions given below: a) p(x) = (5/8) log [base(a)]x b)

algebra 2
log(base 2)csc(x) = log(base 4)csc(4x^2) I tried doing the log(base a)b = logb/loga but I can't get past that because I'm not sure what to do after that. How do I set it up so I get like cscx=? or something so I'm able to solve for multiple values of x?

precalculus
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 ntio is of the form F(x) = b^x, then 2 = b^(1/3) Cube both

Calc
Find the derivative of: 1. Xlog base e (log base e X) 2. log base x 7 3. (sinh x)^2  (cosh x)^2

Math  Logarithmic
log_5[log_4(log_3(x))] = 1 log_5 = log with the base of 5 log_4 = log with the base of 4 log_3 = log with the base of 3 Answer: 3^1024 Too many logs in one equation. . .I don't know how to solve it

logarithms
Ive been staring at this problem for like a half hour now and I cant figure out where to even begin... log(base x)4 + log(base 8)squareroot(x) = 4/3 solve for x any help appreciated

advanced algebra
we are working with logarithms and i don't understand them at all! I get the basic content but then it gets a little more advanced, and I get completely confused. There's one in particular that I have NO idea how to do. Help please?! Simplify: 3 ^

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.

pre cal
(1/3)LN27 + 2LNx = LN(2x) i think i just need help getting started. I assume that your LN notation is log to base e. I will call it ln. (1/3)ln 27 = ln (27)^(1/3) = ln 3, (since 27^(1/3) is the cube root of 27). Therefore ln 3 + 2 ln x = ln (3 x^2) = ln

Calculus
Find the inverse of each relation: y = (0.5)^(x+2) and y = 3log base 2 (x3) + 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 x2. Can someone tell me why it would end up being x2

Precalc
1. 1/3log base 8 of (x+1)=2log base 8 of 3(2/3)log base 8 of (x+1) 2. 2^x+8 times 2^=x all over 2 = 3 3. if log base a of 3= x and log base a of 2 = y, find each of thefollowing in terms of x and y log base a (18a^3) thanks!!

math
Use the Laws of logarithms to rewrite the expression log(base 2)(11x(x9)) in a form with no logarithm of a product, quotient or power. After rewriting we will have: log(base 2)A+log(base 2)x+log(base 2)f(x) What is A and what is f(x)?

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

precalc
Solve: round to the thousandths if necessary! 1) 4^3/4x+5 = 12 2) log(x1) + log x = log 6 3) 2log(base 4) 5  log(base 4) x + log(base 4) 3  log(base 4) 7 = 1/2

precalc help
Find the exact value without a calc 1. log base 3 of 8 times log base 8 of 9. I started by changing both bases to 10 but don't know what to do from there. 2. e ^ log base e^2^9. I hope that isnt confusing. My teacher said we are suppose to get the bases

mathlogs
1. logaB = 2 and logbC = 4, evaluate logcA *the lowercase letters are bases ie. log(base a)B 2. solve for x: (log(base 2)x))^3 = log(base 2)x

LOGARITHMS
HI THE QUESTION STATES THAT ONE SHOULD CALCULATE THE LOGS WITHOUT THE USE OF A CALCULATOR...OKAY MY PROBLEM IS THIS... 2 3 2log 8 + 2log 8 what should i do? i had come to the piont of... 4 5 log 8 + log 8 But what's to do now i don't know..Think u can

log equation graph
How do you graph y= log (base 5)(x)? The written question is: Sketch above equation by first describing the transformations performed on the equation y= log (base 5)(x) And what is the inverse function? x=log (base 5)(y)?

graphing
How do you graph y= log (base 5)(x)? The written question is: Sketch above equation by first describing the transformations performed on the equation y= log (base 5)(x) And what is the inverse function? x=log (base 5)(y)?

Algebra 2
I am trying to find the inverse of these functions. Can someone please check my answers and tell me how to do number 2? 1. y=7^x y=log base 7 x 2. y=log base 1/2 x 3. y=2^(x)3 y=2^(x+3) 4.y=6+log x

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 crossmultiply hence a^2r^2 = a^2r^2 L.H.S=R.H.S

Algebra
In the logarithmic expression . . . log(base 4) 8 , how does the base 4 become base 2? Here is how it is suppose to be worked out: log(base2)8 / log(base2)4 => log(base2)2^3 / log(base2)2^2 => 3/2

Algebra 2
solve for x: 3^2x+3=7^x+1 I did 2x+3=log0f3(7)+ logof3(7) (2log of 3(7))x=log of 3(7)3 x=log of 3 (7)+log of 3 (3^3)/log 0f 3 (3^2)log of 3 (7) x=log of 3 (71/3^3)/log of 3(9/7) log of 3(7/27)/log of 3(9/7) answer log of 9/7(7/27) Is this correct?

math
I need an expression written for the following logs using "sum, difference, or multiple of logarithms." a) log[base(2)] ((x^2)  9)/(x^3))^3 b) log[base(a)]5a^4 Hopefully they are clearly written. thanks. roberto

Trigonometry
Solve for x to the nearest hundreth and can you explain how you get your answer I don't understand 3^x = 1.295 Your question has nothing to do with trigonometry. You can solve for x by taking the logarithm (to any base) of both sides of the equation. Then

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.

Chemistry
What is the pH of the solution if 0.015 mol of HCl is added to a buffer containing 0.014 mol of RCOOH and 0.033 mol of RCOONa (source of RCOO)? Ka = 2.8E5 I have tried the following: adding 0.014 + 0.015 = 0.029 ph = pka + log (Base/Acid) pH =

Math
Log(base a)(a^4*b)Log(base a)(a*b) is the same as a)4 b)3 c)3a d)a^3 I got the answer as d since subtracting logs with the same base is division. However, the answer key saids its b, Can someone please help me with this?

Algebra 2
how do not understand how to do this Log X + Lob (X3) = 1 I know I do this Log X(X3)=1 then I do this Log X^(2)  3X = 1 then I do this 2 Log (X3X) = 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 =

Math 12
Hey everyone; There are some questions on my review I am having trouble with. 4. Evaluate each logarithm. g)log base 5 square root 5 I can't figure out how to do square roots... h)log base 3 1 I got 3, but the anwser is 0 Also, directions ask you to write

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? Details

Precalc
solve the equation: log base 10 of x  log base 10 of (74x)=2 Please help i have been stuck on this for awhile!

College Algebra
Solve the logarithmic equation for x. log(base 3)(x+6)  log(base 3)(x+1)=1 urgent! help!

Chemistry
Strong base is dissolved in 535 mL of 0.200 M weak acid (Ka = 3.16 × 105) to make a buffer with a pH of 4.04. Assume that the volume remains constant when the base is added. HA (aq)+ OH^(aq) > H2O(l) + A^(aq) Calculate the pKa value of the acid and

maths
Solve this logarithmic equation. 3 log 2 base x + log 18 base x = 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)xlog(base 2)6=log(base 2)5+2log(base 2)3 5. Solve 3^(2x) = 9(81^x) 6. Solve 3^(2x)=7^(3x1). Round answer to

check!
here is the question: log5(x4)= 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(x4) = 7x, so 5x 20 =7x

Math  Bases
What is 12 base 5? Would you just divide 12 by five and get 2 (but then what about the remainder) If you are refering to logs, 12 base 5 means log of 12 to the base 5. Call it x. 5^x = 12. x = log 12/log 5 (any log base can be used) x = 1.07918/0.69897 =

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

math
i have 2 math questions i don't understand so if you could help me i would like that. Log base 3 64log base 3 (8/3)+log base 3 2=log base 3 4r Log base 6 (b^2+2)+logbase6 2=2

Precalculus
I'm studying for my precalc exam and have completed 42 practice problems. I have 3 I need to answer that I can't. Please help. What is the base of the function G(x) = log subscript b x if it's graph has points (16,4)? Using the properties of logarithms how

College Alegebra
I know I have to take the log of both sides, but I don't seem to get how they work out! Can anyone explain how to do 3e^(1+x) = 2 AND 10^(2x+3) = 280 If you walk me through one I should be able to figure out the other. Hopefully... I think you need to go

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

PreCalculus
Laws of Logarithms Without using a calculator use the change of base rule to evaluate 1. a) log(subscript8)32(hint use base 2) =log(subscript2 32)/log(subscript2 8) = 5/3 b) log(subscript36)1296. This one doesnt even give you a hint, so how do you know

logarithm
If log base 2 of x and log base 2 of y are distinct positive integers and log base x of 2 plus log base y of 2 equal to 0.5. xy=?

Algebra
How can you find log base 3 of 242/5 using the given information without a calculator? log base 3 of 10 = 2.1 log base 3 of 11 = 2.2 log base 3 of 4 = 1.3

need math help asap (logs) !!!
Create a question that will use all four Log Operations and four Basic Log properties. The four log properties are: Logb 1=0; logbB=1; logbB^x=x; b^logbx=x the final answer must be X=e^pi where e is the natural log base = 2.718 be creative. Start with ln x

Math
these are some problems i do not get any help is appreciated. These are copied exactly from the worksheet so i don't think i wrote anything wrong. Please explain it for me and could i get the answer thanks (: Log7 x= ½ log7 36 (log base 7) log x=2log 5+

precalculus
What is the domain and range of log3 (1x)? I will be happy to critique your thinking. To assist you, consider log (4) log (0) log 25 Those are to the base 10, changing to another base just changes the numbers, not the function.

maths need help
If Log (a+3) (base 9)  log b(base 9)= c + (1/2) and log (a3) (base 3) + log b (base 3)=c  1. show that a^2=9 + 27^c and find the possible values of a and b when c=1

Algebra 2
Can you please explain step by step on how to do this problem? Condense the expression. 2(log base 6 of 15  log base 6 of 5) + 1/2 log base 6 of 1/25

Algebra 2
Can you please explain step by step on how to do this problem? Condense the expression. 2(log base 6 of 15  log base 6 of 5) + 1/2 log base 6 of 1/25

Review of Logs
I can't seem to get the answer to this; the answer key says log(base 8)6 Write as a single logarithm log(base 8)42log(base 8)3  log(base 8) 6 I'm hoping the key is wrong :) Thank you for your help!

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

algebra 2 logs and trig
log(base 2)cotx  2log(base 4)csc2x = log(base 2)cosx the answer should be x = pi/3, 5pi/3 not sure how to work it out though, any help? I tried canceling the bases but that led to a dead end.

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..

Algebra2
Combine, rewrite & solve: 4 log base 9 of 3 = x log base x of 12 + log base x of 18 = 3

Calculus
Please help simplify this expression: 2 log (base 4) ^9  log (base 2) ^3 The answer should be log(base 2) ^3

Advanced Math
log10x + log10(x+1)=1 In other words log base 10 + log base 10(x+1)=1 I need to show it algebraically not using calculator Thanks a lot !

Math
How do you write ln(n) in log form? I know that you can convert log of some base by doing ln of the variable over ln of the base, but I don't know how to do the opposite.

Logarithms
if log base 10 of 2 = .301 then what is log base of 10 of 2000? I know how to solve with a calculator but I'm having a hard time doing it without one.

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

Math
can someone please look over this and tell me if I made a mistake? log with a base of 3(−9) = 2x log with a base of 3(9) = 2x 2=2x x=1 I'm pretty sure I did it right but just incase please look over and let me know if and where I went wrong. Thanks!

Algebra 2
Log base 5 of 16 cubed. Times log base 11 of 6 squared. Equals logx.

Algebra 2 ..
Simplify. 1. Log base 4 of 256^2 IS THE ANSWER 8....IF SO AM I SMART? 2. Log of 45 ^x Is the answer 1.65X? 3. Log base 6 of 12 ^(x+1) Is the answer 1.39x+1.39?

Algebra 2
Use the laws of logarithms to condense the following expressions. log base 3 of 2 + 2 log base 3 of x

Math
What are the possible solutions of 2 log base 2 𝒂 = 10 − 2 log base 2 𝒃, where 𝒂 and 𝒃 are integers? Show work.

trig
If a, b are the solutions of the equation log base 3 (52x)+ log base 3 (5+2x)=2 find the value of the product ab.

math 12 logarithms
How would I go about proving 1/log a +1/log a = 1/log base 100 a. Any help would be greatly appreciate. Thanks

Logarithm Please Help
x and y are positive real numbers that satisfy log(base)x y + log(base)y x = 17/4 and xy=288√3. If x+y=a+b√c, where a, b and c are positive integers and c is not divisible by the square of any prime, what is the value of a+b+c?

Calculus
log base 4 of 8/log base 8 of 16 question is to simplify can you rewrite it this way? 4^x = 8  8^x = 16

Math  logs
I need help solving this because it involves 2 bases: log (base 2) [log (base 5) 25]= ???