Precalc
posted by Rebekah .
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!!

1.
omitting all the base 8 stuff, we have
1/3 log(x+1) = 2log3  2/3 log(x+1)
log(x+1) = 2log3
log(x+1) = log9
x+1=9
x=8
2.
not sure what the extra = means.
(2^x + 8*2^x)/2 = 3
9*2^x/2 = 3
9*2^x = 6
2^x = 3/2
x = ln(3/2)/ln2
May be a typo here; it's an odd answer
3.
omitting all the base a stuff,
log(18x^3) = log18 + loga^3
= log9+log2+3loga
= 2log3 + log2 + 3loga
= 2x+y+3 
oops it was 2^x
im confused why would you omit the bases? 
just for readability. Got tired of typing it in. And, until you need to resolve the base, it doesn't really matter. In #1, the equations work regardless of base, since we are working with logs on both sides of the equation.
In #3, the base didn't matter until we could use it to say that log_a(a) = 1
For #2, I suspected it might have been 2^x, and it helps a lot!
(2^x + 8*2^x)/2 = 3
2^x + 8/2^x = 6
if you let u = 2^x, then you have
u+8/u = 6
u^2 + 8 = 6u
u^2  6u + 8 = 0
(u4)(u2) = 0
u=4 or u=2
2^x=4 or 2^x=2
x=2 or x=1
Respond to this Question
Similar Questions

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) … 
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 … 
Algebra
How can you find log base 3 of 242/5 using the given information without a calculator? 
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 … 
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
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)? 
Algebra 2
Explain the difference between log base b (mn) and ( log base b of m)(log base b of n). Are they equivalent? 
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). … 
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 
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?