SOLUTION: Without using a calculator, show that (log sqrt(64) + log sqrt(27) - log sqrt(125))/(log12 - log5) = 3/2

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Question 1043691: Without using a calculator, show that (log sqrt(64) + log sqrt(27) - log sqrt(125))/(log12 - log5) = 3/2
Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Without using a calculator, show that (log sqrt(64) + log sqrt(27) - log sqrt(125))/(log12 - log5) = 3/2
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log[8*3sqrt(3)/5sqrt(5)] = (3/2)/log[12/5]
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log[(24/5)sqrt(3/5) = log(12/5)^(3/2)
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log[(24/5)sqrt(3/5)] = log(2^2*3/5)^(3/2)
log[(24/5)sqrt(3/5)] = log(2*sqrt(3/5))^3
log[(24/5)sqrt(3/5)] = log(8*3/5)sqrt(3/5))
log[(24/5)sqrt(3/5)] = log[(24/5)sqrt(3/5]
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Cheers,
Stan H.
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Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
show that (log sqrt(64) + log sqrt(27) - log sqrt(125))/(log12 - log5) = 3/2
((1/2)log(64) + (1/2)log(27) - (1/2)log(125))/(log(12) - log(5)) = 3/2
Multiply by 2
((log(64) + log(27) - log(125))/(log(12) - log(5)) = 3
log(64*27/125)/log(12/5) = 3
log(1728/125) = 3log(12/5) = log(1728/125)
QED