SOLUTION: i have tried this problem several times and i just cant get an answer that works when i plug it back in. so far i have gotten 2/3 and 17/18 (2^x)*(8^(x+1))=16^(1/3) help plea

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: i have tried this problem several times and i just cant get an answer that works when i plug it back in. so far i have gotten 2/3 and 17/18 (2^x)*(8^(x+1))=16^(1/3) help plea      Log On


   

Question 554298: i have tried this problem several times and i just cant get an answer that works when i plug it back in. so far i have gotten 2/3 and 17/18
(2^x)*(8^(x+1))=16^(1/3)
help please!
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
%282%5Ex%29%2A%288%5E%28x%2B1%29%29+=+16%5E%281%2F3%29 Replace: 8+=+2%5E3 and 16+=+2%5E4
%282%5Ex%29%2A%282%5E3%29%5E%28x%2B1%29+=+2%5E%284%281%2F3%29%29 Simplify.
%282%5Ex%29%2A%282%5E%283x%2B3%29%29+=+2%5E%284%2F3%29 Add the exponents on the left side.
2%5E%284x%2B3%29+=+2%5E%284%2F3%29 Since the bases (that's 2) are equal, the exponents are equal, so...
4x%2B3+=+4%2F3 Multiply through by 3 to clear the fraction.
12x%2B9+=+4 Subtract 9 from both sides.
12x+=+-5 Divide by 12.
x+=+-5%2F12
Check:
%282%5Ex%29%2A%288%5E%28x%2B1%29%29+=+16%5E%281%2F3%29 Substitute x = -5/12
2%5E%28-5%2F12%29%2A%288%5E%287%2F12%29%29+=+16%5E%281%2F3%29
2%5E%285%2F12%29%2A%282%5E%2821%2F12%29%29+=+2%5E%284%2F3%29 Simplify.
%282%5E%2821%2F12%29%29%2F%282%5E%285%2F12%29%29+=+2%5E%284%2F3%29
2%5E%2816%2F12%29+=+2%5E%284%2F3%29
2%5E%284%2F3%29+=+2%5E%284%2F3%29