Question

Solve : $2^{lo{g}_{3}5}-5^{lo{g}_{3}2}.$

Answer 1

$2^{{\log }_{3}5}-5^{{\log }_{3}2}=2^{\frac{{\log }_{2}5}{{\log }_{2}3}}-5^{\frac{{\log }_{5}2}{{\log }_{5}3}}=\frac{5}{3}-\frac{2}{3}=\frac{3}{3}=1$