Question

Logarithm of $32\sqrt[5]{54}$ to the base $2\sqrt{2}$ is

• A. 3.6
• B. 5
• C. 5.6
• D. None of these

Answer 1

The correct option is A 3.6

Let x be the required logarithm , then by definition $(2\sqrt{2}{)}^x=32\sqrt[5]{54}\Rightarrow {\left({2.2}^{\frac{1}{2}}\right)}^x=2^5{.2}^{\frac{2}{5}};$
$\therefore 2^{\frac{3x}{2}}=2^{5+\frac{2}{5}}$
Here, by equating the indices, $\frac{3}{2}x=\frac{27}{5}$
$\therefore x=\frac{18}{5}=3.6$