# Exponential & Logarithmic Equations

• Mar 14th 2013, 09:26 AM
paigesisco
Exponential & 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 AM
BobP
Re: Exponential & Logarithmic Equations
Make use of one of the rules of logs, $\log a^{k} = k\log a.$
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 AM
Plato
Re: Exponential & Logarithmic Equations
Quote:

Originally Posted by paigesisco
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.

Write it as $2^{2x+4}=(2^{-2x-3})(3^{-2x-3})$
• Mar 14th 2013, 10:04 AM
Shakarri
Re: Exponential & Logarithmic Equations
Another way to do it,

Remember that

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

So we have

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

then

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