Solve $2^x\cdot 6^{x-2}=5^{2x}\cdot 7^{1-x}$ I have to solve this equation, $2^x\cdot 6^{x-2}=5^{2x}\cdot 7^{1-x}$. Now, I started by taking logs on both sides which gives me this funny looking equation 
$x\log{2}+(x-2)\log(2\cdot3)=2x\log(\frac{10}{2})+(1-x)\log{7}$
I have been stuck on this step for a while now and can't see how I can go further from here. Is there a way out?

$$\begin{matrix}
2^x.6^{x-2} & = & 5^{2x}.7^{1-x} \\ 
\left(\dfrac{2*6*7}{5^2}\right)^x & = & 6^2 * 7 \\ 
\left(\dfrac{84}{25}\right)^x & = & 252 \\ 
x & = & \dfrac{\ln\left(252\right)}{\ln\left(\dfrac{84}{25}\right)}
\end{matrix}$$
