Question

Find the value of $3^{\frac{4}{{\log }_{2}9}}+{27}^{\frac{1}{{\log }_{49}9}}+{81}^{\frac{1}{{\log }_{4}3}}$

Answer 1

$3^{\frac{4}{{\log }_{2}9}}+{27}^{\frac{1}{{\log }_{49}9}}+{81}^{\frac{1}{{\log }_{4}3}}$

$=3^{4{\log }_{9}2}+{27}^{{\log }_{9}49}+{81}^{{\log }_{3}4}$

$=3^{2{\log }_{3}2}+3^{3{\log }_{3}7}+3^{4{\log }_{3}4}$

$=3^{{\log }_{3}4}+3^{{\log }_{3}343}+3^{4{\log }_{3}256}$

$=4+343+256=603$