What is logarithm of ` 32 root(5) 4" to the base "2sqrt2`?

Explanation

To find the logarithm of \( 32 \sqrt[5]{4} \) to the base \( 2\sqrt{2} \), we can follow these steps:

### Step 1: Rewrite the expression
We start by rewriting the expression \( 32 \sqrt[5]{4} \) in terms of powers of 2.

\[ 32 = 2^5 \quad \text{and} \quad 4 = 2^2 \implies \sqrt[5]{4} = (2^2)^{1/5} = 2^{2/5} \]
...