Logarithm problems

$\begin{aligned} \log_5 x + \log_7 x & = \log_{25} x \\ \frac {\log x}{\log 5} + \frac {\log x}{\log 7} & = \frac {\log x}{\log 25} & \small \blue{\text{Since }\frac 1{\log 5} + \frac 1{\log 7} \ne \frac 1{\log 25}} \\ \implies \log x & = 0 \\ \implies x & = \boxed 1 \end{aligned}$

Probably the question asks for the value of $x$ satisfying the equation $log_5x+log_7x=log_{25}x$ . If this is the case then $\dfrac{ \log x}{\log 5}+\dfrac{\log x}{\log 7}=\dfrac{\log x}{\log {25}}$ or $\log x=0$ or $x=\boxed 1$