The question wants me to solve:
3^(x+2) - 4 = 12
So:
3^(x+2) = 8
What do I do next?
Any help is appreciated.
$\displaystyle 3^{x+2} - 4 = 12$
Ok....hopefully this helps and you know the log properties
$\displaystyle 3^{x+2}= 16$
$\displaystyle \ln3^{x+2} = \ln 16$
$\displaystyle (x+2)\ln3 = \ln 16$
This is one way, a little longer...
$\displaystyle x\ln3+2\ln3 = \ln 16$
$\displaystyle x\ln3 = \ln 16 - 2\ln3$
$\displaystyle x\ln3 = \ln (\frac{16}{9})$
$\displaystyle x= \frac{\ln (\frac{16}{9})}{\ln3}$
Or going back to the line before my comment....
$\displaystyle (x+2)\ln3 = \ln 16$
$\displaystyle x+2 = \frac{\ln 16}{\ln3}$
$\displaystyle x = \frac{\ln 16}{\ln3}-2$
and both....
$\displaystyle x = \frac{\ln 16}{\ln3}-2$ and $\displaystyle x= \frac{\ln (\frac{16}{9})}{\ln3}$ = .5237190143....