Solving exponential equations using logarithms This is the equation that I am having troubles with:  
$$\large x^{\large\log_{10}5}+5^{\large\log_{10}x}=50$$
So the first thing I do, I logarithm the whole expression with $\log_{10}$.
So I get:
$ {\log_{10} 5}  \times {\log_{10} x} + {\log_{10} 5}  \times {\log_{10} x} = {\log_{10} 50}$   
When I solve this one for $x$, I get that $x = 16$, which is totally incorrect because it is supposed to be $100$. Can anyone tell me what am I doing wrong or show me how to solve this equation?

Let $y=x^{\large\log_{10}5}$, then
$$
\log_{10}y=(\log_{10}5)(\log_{10}x)=\log_{10}5^{\large\log_{10}x}\color{red}{\quad\Rightarrow\quad} y=5^{\large\log_{10}x}.
$$
Hence
\begin{align}
x^{\large\log_{10}5}+5^{\large\log_{10}x}&=50\\
5^{\large\log_{10}x}+5^{\large\log_{10}x}&=50\\
2\times5^{\large\log_{10}x}&=50\\
5^{\large\log_{10}x}&=25\\
5^{\large\log_{10}x}&=5^2\color{red}{\quad\Rightarrow\quad}\log_{10}x=2\color{red}{\quad\Rightarrow\quad}\large\color{blue}{ x=10^2=100}.
\end{align}
