SOLUTION: I must solve the following equation, and then round the answer to the nearest hundreth, while using the Log way. 1+8(0.43)^2u=3 I placed Log in front of both equations like 2uLog

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Question 70761This question is from textbook Algebra 2 Explorations and Applications
: I must solve the following equation, and then round the answer to the nearest hundreth, while using the Log way. 1+8(0.43)^2u=3
I placed Log in front of both equations like 2uLog(0.43)=Log(3/9). However I keep getting a completely different answer than what the book has provided, which is .82. Please solve this solution, thanks.This question is from textbook Algebra 2 Explorations and Applications

Found 2 solutions by Earlsdon, stanbon:
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for u:
1%2B8%280.43%29%5E%282u%29+=+3 Subtract 1 from both sides of the equation.
8%280.43%29%5E%282u%29+=+2 Next, divide both sides by 8.
%280.43%29%5E%282u%29+=+2%2F8 Simplify.
%280.43%29%5E%282u%29+=+0.25 Now apply the logarithms.
Log%280.43%29%5E%282u%29+=+Log%280.25%29 Apply the power rule for logarithms to the left side.
2uLog%280.43%29+=+Log%280.25%29 Divide both sides by Log%280.43%29
2u+=+%28Log%280.25%29%29%2FLog%280.43%29 Now divide both sides by 2.
u+=+%281%2F2%29%28%28Log%280.25%29%29%2FLog%280.43%29%29 Evaluate the logs using your calculator or log tables.
u+=+%281%2F2%29%281.64%29
u+=+0.82 To the nearest hundredth.

Answer by stanbon(48535) About Me  (Show Source):
You can put this solution on YOUR website!
1+8(0.43)^2u=3
Subtract 1 from both sides to get:
8(0.43)^2u=2
log[8(0.43)^2u] =log2
log 8 + log(0.43)^2u =log 2
2u[log0.43] = log 2 - log8
2u[log0.43] = log(1/4)
2u = log(1/4)/log(0.43)
2u = 1.64258
u=0.82
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Cheers,
Stan H.