Solve `(log)_(2x)2+(log)_4 2x=-3//2.`

Explanation

To solve the equation \( \log_{2x} 2 + \log_{4} 2x = -\frac{3}{2} \), we will follow these steps:

### Step 1: Rewrite the logarithms using the change of base formula
Using the property of logarithms, \( \log_a b = \frac{\log b}{\log a} \), we can rewrite the equation:

\[ \log_{2x} 2 = \frac{\log 2}{\log(2x)} \quad \text{and} \quad \log_{4} 2x = \frac{\log(2x)}{\log 4} \]
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