# Thread: Double check my answers? Thank you!~

1. ## Double check my answers? Thank you!~

Solve the following equation:

$12^x=(3^x)(2^{x+7})$

I did it this way. Is it correct?

$(3^{x})(4)=(3^{x})(2^{x+7})$
$(3^{x})(2^2)=(3^{x})(2^{x+7})$
$(3^{x-x})(2^{x+7-2})=1$
$2^{x+5}=1$
$2^{x+5}=2^0$
$x+5=0$
$x=-5$

Thank you very much!

2. ## Re: Double check my answers? Thank you!~

But the answer at the back is 7. If my answer is wrong how do i solve it then? thanks a lot!

3. ## Re: Double check my answers? Thank you!~

in a case like this, just sub in the value of x and solve both sides and see if they are equal.

4. ## Re: Double check my answers? Thank you!~

Originally Posted by pumbaa213
Solve the following equation:

$12^x=(3^x)(2^{x+7})$

I did it this way. Is it correct?

$(3^{x})(4)=(3^{x})(2^{x+7})$
$(3^{x})(2^2)=(3^{x})(2^{x+7})$
$(3^{x-x})(2^{x+7-2})=1$
$2^{x+5}=1$
$2^{x+5}=2^0$
$x+5=0$
$x=-5$

Thank you very much!
$\displaystyle 12^x$ is not the same as $\displaystyle 4*3^x$

You should solve it like this:

$\displaystyle 12^x=(3^x)(2^{x+7})$

But $\displaystyle 2^{x+7}=(2^x)(2^7)$

So you have

$\displaystyle 12^x=(3^x)(2^x)(2^7)=(6^x)(2^7)$

Can you solve that?

Let us know if you need more help!

5. ## Re: Double check my answers? Thank you!~

Thank you sakonpure6 and Cesc1 for your guys help! I think i'll still need more assistance on how to solve the question. I've tried but im still not sure what to do after this step.

12^x=(6^x)(2^7)

How should i split 12^x to get a 6 and 2? Thank you!!

6. ## Re: Double check my answers? Thank you!~

Originally Posted by pumbaa213
Thank you sakonpure6 and Cesc1 for your guys help! I think i'll still need more assistance on how to solve the question. I've tried but im still not sure what to do after this step.

12^x=(6^x)(2^7)

How should i split 12^x to get a 6 and 2? Thank you!!
$\displaystyle 12^x=(6^x)(2^7)$

But $\displaystyle 12^x=(6*2)^x=(6^x)(2^x)$

So $\displaystyle (6^x)(2^x)=(6^x)(2^7)$

Divide both sides by $\displaystyle 6^x$ and you get

$\displaystyle 2^x=2^7$

So $\displaystyle x=7$

7. ## Re: Double check my answers? Thank you!~

Thanks for the reply. But mind if i ask, wont (6^x) x (2^x) give you 12^x^2?
Sorry if im wrong. I had a huge break from math! ><

8. ## Re: Double check my answers? Thank you!~

WAIT! I get it!! ^V^
THANKS EVERYBODY! YOU'VE bEEN OF GREAT HELP! <3