SOLUTION: Hi. I had a question about solving this log problem. I asked this a few hours so I'm assuming the person who took on this problem wasn't able to answer it. Thanks in advance. Here

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hi. I had a question about solving this log problem. I asked this a few hours so I'm assuming the person who took on this problem wasn't able to answer it. Thanks in advance. Here       Log On


   

Question 709009: Hi. I had a question about solving this log problem. I asked this a few hours so I'm assuming the person who took on this problem wasn't able to answer it. Thanks in advance. Here is the problem:
Use logarithms to solve the equation for x. [Hint: take logs of both sides and simplify]
2^x=6\times 3^x
x= ________
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
I'll take this part of the way through the solution steps.

You seem to ask to solve, 2%5Ex=6%2A3%5Ex

I'll use "natural logs" because it's less effort for the typesetting on this algebra.com system, less missing grouping symbols in the text needed.

ln%282%5Ex%29=ln%286%29%2Bln%283%5Ex%29
xln%282%29=ln%286%29%2Bxln%283%29
-ln%286%29=xln%283%29-xln%282%29
-ln%286%29=x%28ln%283%29-ln%282%29%29
%28-ln%286%29%29%2F%28ln%283%29-ln%282%29%29=x, and I stop here, so maybe you could finish. This is an expression using only constants equal to the variable, x.