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?

It's $$x\ln2+(x-2)\ln6=2x\ln5+(1-x)\ln7,$$ which gives
$$x=\frac{2\ln6+\ln7}{\ln2+\ln6-2\ln5+\ln7}$$ or
$$x=\log_{\frac{84}{25}}252$$
