If ` log_(a) 3 = 2 and log_(b) 8 = 3," then prove that "log_(a) b= log_(3) 4`.

Explanation

To prove that \( \log_a b = \log_3 4 \) given that \( \log_a 3 = 2 \) and \( \log_b 8 = 3 \), we can follow these steps:

### Step 1: Rewrite the given logarithmic equations
From the first equation, \( \log_a 3 = 2 \), we can rewrite it using the change of base formula:
\[ \log_a 3 = \frac{\log 3}{\log a} = 2 \]
This implies:
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