Find the value of `2log2/5 +3 log25/8 -log 625/128`

Explanation

To solve the expression \(2\log\frac{2}{5} + 3\log\frac{25}{8} - \log\frac{625}{128}\), we will use properties of logarithms. Let's break it down step by step.

### Step 1: Apply the Power Rule of Logarithms
Using the property \(m \cdot \log_b(a) = \log_b(a^m)\), we can rewrite the expression:

\[ 2\log\frac{2}{5} = \log\left(\frac{2}{5}\right)^2 = \log\frac{4}{25} \]
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