Question

Find the value of the following:

${81}^{\frac{1}{{\log }_{5}3}}$

Answer 1

Let $x={81}^{\frac{1}{{\log }_{5}3}}$

$\therefore x={81}^{\frac{1}{{\log }_{5}3}}=(3^4{)}^{{\log }_3^5}=3^{{\log }_3{5}^4}=5^4=625$