Can someone help me with this question of finding x as exponent? The equation is:
$$6^{x+1} - 6^x = 3^{x+4} - 3^x$$
I need to find x. I forgot how to use logarithm laws. Help would be appreciated. Thanks.

Let $$3^x=t, 2^x=u$$
Your original equation becomes $$6ut-ut=3^4t-t\Rightarrow5ut=t(3^4-1)\Rightarrow\\ u=\frac{3^4-1}{5}\Rightarrow 2^x=16\Rightarrow x\ln2=\ln16\Rightarrow\\x\ln2=\ln2^4=4\ln2\Rightarrow\\x=4$$
