Question

Evaluate:${\log }_{49}343$

Answer 1

Let $a={\log }_{49}343$

$={\log }_{7^2}{7}^3$

We know that, ${\log }_{a^n}{a}^m=\frac{m}{n}{\log }_{a}a$

$a=\frac{3}{2}{\log }_{7}7$

Since ${\log }_{a}a=1$

$a=\frac{3}{2}$

${\log }_{49}343=\frac{3}{2}$