Question

Find the value of $2^{{\log }_{3}5}-5^{{\log }_{3}2}$.

Answer 1

Here, $2^{{\log }_{3}5}=2^{\frac{{\log }_{2}5}{{\log }_{2}3}}={\left(2^{{\log }_{2}5}\right)}^{{\log }_{3}2}=5^{{\log }_{3}2}$

Hence, $2^{{\log }_{3}5}-5^{{\log }_{3}2}=0$