4^(x+2)=6^(-2x-3)

I am completely clueless how to do this problem because neither my teacher nor my book explained it very well. Please HELP

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- Mar 14th 2013, 09:26 AMpaigesiscoExponential & Logarithmic Equations
4^(x+2)=6^(-2x-3)

I am completely clueless how to do this problem because neither my teacher nor my book explained it very well. Please HELP - Mar 14th 2013, 09:34 AMBobPRe: Exponential & Logarithmic Equations
Make use of one of the rules of logs, $\displaystyle \log a^{k} = k\log a.$

It doesn't matter what base you choose, the rule works for any base.

Take logs of your equation, apply the rule and then solve for x. - Mar 14th 2013, 09:35 AMPlatoRe: Exponential & Logarithmic Equations
- Mar 14th 2013, 10:04 AMShakarriRe: Exponential & Logarithmic Equations
Another way to do it,

Remember that

$\displaystyle 6= 4^{log_4 {6}}$

So we have

$\displaystyle 4^{x+2}=4^{(log_4 {6})\cdot(-2x-3)}$

then

$\displaystyle x+2= (log_4 {6})\cdot(-2x-3)$