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.

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- Dec 18th 2009, 11:54 AMiluvmathbutitshardHow 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. - Dec 18th 2009, 12:02 PMDinkydoe
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 - Dec 18th 2009, 12:30 PMJSB1917
$\displaystyle 3^{x+2} - 4 = 12$

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.... - Dec 18th 2009, 12:34 PMiluvmathbutitshard
Thank you so much. This really helps. :)