SOLUTION: Solve: 8^(4x-3)= 1/16, find the exact answer.

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Question 34528: Solve:
8^(4x-3)= 1/16, find the exact answer.
Found 2 solutions by venugopalramana, josmiceli:
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
8^(4x-3)= 1/16,
(2^3)^(4X-3)=1/(2^4)=2^(-4)
2^(12X-9)=2^(-4)
12X-9=-4
12X=-4+9=-5
X=-5/12
find the exact answer.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
8%5E%284%2Ax+-+3%29+=+1%2F16
note that x%5E%28a%2Bb%29+=+x%5Ea+%2A+x%5Eb
8%5E%284%2Ax%29+%2A+8%5E%28-3%29+=+1%2F16
multiply both sides by 8^3
8%5E%284%2Ax%29+=+8%5E3+%2F+16
8%5E%284%2Ax%29+=+32
take log base 10 of both sides
log%288%5E%284%2Ax%29%29+=+log%2832%29
note that log+x%5Ea+=+a%2Alog%28x%29
4+%2A+x+%2A+log%288%29+=+log%2832%29
x+=+log%2832%29+%2F+%284+%2A+log%288%29%29
x+=+1.50515+%2F+%284+%2A+.90309%29
x+=+1.50515+%2F+3.61236
x+=+.41667
check this by subbing in the original equation
I get 8%5E%28-4%2F3%29+=+1%2F16
this is true- checks
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note also- 32+=+8%5E%285%2F3%29
8%5E%284%2Ax%29+=+8%5E%285%2F3%29
4%2Ax+=+5%2F3
x+=+5%2F12
this is a more "exact" answer, since there is no rounding to a certain number
of decimal points