Log base change rule

[13mathBoss]

How to solve this one???
I can't do the deduce part...
Is there something wrong with this problem??? ? However I applied this deduce part to hence part I can get the relevant answer...
Please solve this... ?

 

[HallsofIvy]

The main difficulty is that this problem is non-sense! Since the conclusion has all logarithms to base "a" there is no need for a "change of base" rule. More importantly the conclusion, that \(\displaystyle log_a(n^{x^m})= \frac{m}{n}log_a(x)\)$ is NOT TRUE.

Take x= 1, m and n any positive numbers. \(\displaystyle x^m= 1^m= 1\) so \(\displaystyle log_a(n^{x^m})= log_a(n^1)= log_a(n)\) but \(\displaystyle \frac{m}{n}log_a(x)= \frac{m}{n}log_a(1)= 0\).