Logarithmic Equation Real Solutions

RHS $= 2 \log_{25}(2x - 4) = 2 \cdot \frac{1}{2} \log_5(2x - 4) = \log_5(2x - 4)$. So $\log_5(x - 2) = \log_5(2x - 4)$. Equating arguments: $x - 2 = 2x - 4 \implies x = 2$.

Checking domain: For $x = 2$, $x - 2 = 0$, but the argument of a logarithm must be strictly positive ($x - 2 > 0$). Thus $x = 2$ is extraneous and invalid. Therefore, there are 0 valid real solutions.