Question

Evaluate ;$2^{{\log }_{3}5}-5^{{\log }_{3}2}$

Answer 1

Given : $2^{{\log }_{3}5}-5^{{\log }_{3}2}$

Let $a=2^{{\log }_{3}5}-5^{{\log }_{3}2}$

We know that, $a^{{\log }_{b}c}=c^{{\log }_{b}a}$

$\therefore a=5^{{\log }_{3}2}-5^{{\log }_{3}2}$

$\therefore a=0$