# Thread: How do I solve this?

1. ## How do I solve this?

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.

2. I hope you are familiar with logarithms

Anyway: Observe that log(8)/log(3) = x+2
And this is equivalent to: log(8)/log(3)-2 = x

3. Originally Posted by iluvmathbutitshard
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....

4. Thank you so much. This really helps.