SOLUTION: find the values of the following without using calculators. (a)log x^3 / log cube root x where (x is not 1) I know the answer for this question, but I'm not sure my wa

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: find the values of the following without using calculators. (a)log x^3 / log cube root x where (x is not 1) I know the answer for this question, but I'm not sure my wa      Log On


   



Question 1183438: find the values of the following without using calculators.
(a)log x^3 / log cube root x where (x is not 1)
I know the answer for this question, but I'm not sure my way of doing it is right. Therefore I need someone nice to help me check.
ok after doing some stuff I ended up with log x cube divide by log x to the power of a fraction 1/3. To get 9 the answer I simply "cancel out" the "common factor" log x and proceed with 3/1/3 (as a fraction) = 9

Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!
.
find the values of the following without using calculators.
(a)log x^3 / log cube root x where (x is not 1)
~~~~~~~~~~~~~~~

The numerator is  log%28%28x%5E3%29%29 = 3*log(x).

The denominator is  log%28%28root%283%2Cx%29%29%29 = log%28%28x%5E%281%2F3%29%29%29 = %281%2F3%29%2Alog%28x%29.

Now make your fraction and cancel the common factor log(x) in the numerator and the denominator.


You will get  3%2F%28%281%2F3%29%29 = 9.      ANSWER

Solved, answered and explained.