Question

The value of ${81}^{\left(\frac{1}{lo{g}_{5}3}\right)}+{27}^{lo{g}_{9}36}+3^{\frac{4}{lo{g}_{7}9}}$ is equal to

• A. 49
• B. 625
• C. 216
• D. 890

Answer 1

The correct option is D 890

${81}^{\left(\frac{1}{lo{g}_{5}3}\right)}+{27}^{lo{g}_{9}36}+3^{\frac{4}{lo{g}_{7}9}}$
$=3^{lo{g}_3{5}^4}+3^{lo{g}_3{36}^{\frac{3}{2}}}+3^{lo{g}_3{7}^{\frac{4}{2}}}$
$=5^4+{36}^{\frac{3}{2}}+7^2=890$