How to solve the equation $ (x-2)^{\log_{100}(x-2)}+\log_{10}(x-2)^5-12 = 10^{2\log_{10}(x-2)}$?

Question

If $\displaystyle (x-2)^{\log_{10^2}(x-2)}+\log_{10}(x-2)^5-12 = 10^{2.\log_{10}(x-2)}$, then value of $x$ is ...

My Try

Let$$\log_{10}(x-2) = y \quad \Leftrightarrow \quad (x-2)=10^y .$$

Then$$(10)^{(y) (\frac{1}{2})(y)}+5y-12=10^{2y} .$$

Now, how can I calculate the value of $y$?

Thanks.