SOLUTION: Solve for x: log(base10)8 - 1/3log(base10)x = log(base10)2 I would really appreciate your help for this problem, Thank You so much.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve for x: log(base10)8 - 1/3log(base10)x = log(base10)2 I would really appreciate your help for this problem, Thank You so much.      Log On


   

Question 29309: Solve for x:
log(base10)8 - 1/3log(base10)x = log(base10)2
I would really appreciate your help for this problem,
Thank You so much.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x: All logs are to the base 10.
log%288%29-%281%2F3%29log%28x%29+=+log%282%29 Add%281%2F3%29log%28x%29 to both sides of the equation.
log%288%29+=+%281%2F3%29log%28x%29+%2B+log%282%29 Subtract log%282%29 from both sides.
log%288%29-log%282%29+=+%281%2F3%29log%28x%29 Apply the "quotient rule" for logarithms to the left side.
log%288%2F4%29+=+%281%2F3%29log%28x%29
log%284%29+=+%281%2F3%29log%28x%29 Multiply both sides by 3.
3log%284%29+=+log%28x%29
log%284%5E3%29+=+log%28x%29
4%5E3+=+x
x+=+64