# Thread: Exponential & Logarithmic Equations

1. ## 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

2. ## Re: 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.

3. ## Re: Exponential & Logarithmic Equations

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

4. ## Re: 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

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