SOLUTION: What are all the values of {{{x}}} in which {{{log(2x,(48*root(3,3)))=log(3x, (162 * root(3,2)))}}}?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: What are all the values of {{{x}}} in which {{{log(2x,(48*root(3,3)))=log(3x, (162 * root(3,2)))}}}?      Log On


   

Question 1114566: What are all the values of x in which log%282x%2C%2848%2Aroot%283%2C3%29%29%29=log%283x%2C+%28162+%2A+root%283%2C2%29%29%29?
Answer by greenestamps(13334) About Me  (Show Source):
You can put this solution on YOUR website!


log%282x%2C%2848%2Aroot%283%2C3%29%29%29=n --> %282x%29%5En+=+48%2Aroot%283%2C3%29
log%283x%2C+%28162+%2A+root%283%2C2%29%29%29=n --> %283x%29%5En+=+162%2Aroot%283%2C2%29

Then

%282x%29%5En%2F%283x%29%5En+=+%2848%2Aroot%283%2C3%29%29%2F%28162%2Aroot%283%2C2%29%29

%282%2F3%29%5En+=+%282%5E%288%2F3%29%29%2F%283%5E%288%2F3%29%29
n+=+8%2F3

Then solve either of the original expressions in exponential form to solve for x:

%282x%29%5E%288%2F3%29+=+48%2Aroot%283%2C3%29
%282%29%5E%288%2F3%29%28x%29%5E%288%2F3%29+=+%282%5E4%29%283%5E%284%2F3%29%29
x%5E%288%2F3%29+=+%282%5E%284%2F3%29%29%283%5E%284%2F3%29%29+=+6%5E%284%2F3%29
x+=+sqrt%286%29

Answer: There is one value -- x=sqrt%286%29 -- that satisfies the given equation.