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.

Divide both sides by $3^x$, which is positive for all $x\in\mathbb R$:
$$6^{x+1} - 6^x = 3^{x+4} - 3^x$$
$$\iff 3^{x}\cdot 3\cdot 2^{x+1}-3^x\cdot 2^x=81 \cdot 3^x - 3^x$$
$$\iff 3\cdot 2^{x+1}-2^x=81-1$$
$$\iff 6\cdot 2^x-2^x=80\iff 5\cdot 2^x =80$$
$$\iff 2^x =16\iff x=\log_2(16)=4$$
