SOLUTION: I've been looking at this question for the past 15 minutes and am having no luck. 8(2^(x+1)) = 2 sqrt(2^x) Thank you for the help!

Algebra ->  Exponents -> SOLUTION: I've been looking at this question for the past 15 minutes and am having no luck. 8(2^(x+1)) = 2 sqrt(2^x) Thank you for the help!      Log On


   

Question 1037110: I've been looking at this question for the past 15 minutes and am having no luck.
8(2^(x+1)) = 2 sqrt(2^x)
Thank you for the help!
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

Instead of doing yours for you, I'll do
one exactly like yours step by step. 
You can then do your equation exactly
the same way:

27%283%5E%282x%2B4%29%29+=+3sqrt%283%5Ex%29

Divide both sides by 3

9%283%5E%282x%2B4%29%29+=+sqrt%283%5Ex%29

Square both sides:

81%283%5E%282x%2B4%29%29%5E2+=+3%5Ex

Multiply the exponents on the left,
the outer 2 by the inner exponent 2x+4:

81%283%5E%284x%2B8%29%29+=+3%5Ex

Write 81 as 34

3%5E4%283%5E%284x%2B8%29%29+=+3%5Ex

Add the exponents of 3 on the left:

3%5E%284%2B%284x%2B8%29%29=3%5Ex

Since the bases are same positive numbers
on both sides and they are not equal to 1,
we may set the exponents equal to each other
and ignore the bases:

4%2B%284x%2B8%29=x

4%2B4x%2B8=x

12%2B4x=x

4x=x-12

3x=-12

x=-4

Now use the above as a model and solve yours 
exactly the same way, step by step.

Edwin