I've been struggling on figuring out these kinds of problems when I need to set f(x) equal to zero and solve for x.

$\displaystyle f(x)={12(1.5^x)}+{12(0.5^x)}$

Here's my thought process:

1) $\displaystyle 0={12(1.5^x)}+{12(0.5^x)}$

2) $\displaystyle \frac{0}{12}=\frac{12(1.5^x)}{12}+\frac{12(0.5^x)} {12}$

3) $\displaystyle {0}={(1.5^x)}+(0.5^x)}$

4) $\displaystyle {0}={(1.5^x)}+(0.5^x)}$; here's where my intuition breaks down. I want to take the log of both sides but I can't due to the zero! Am I going about this kind of problem wrong from the beginning?