Question 253332: log(36)=a and log(125)=b. Find (1/12) in terms of a and b.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! log(36)=a
10^a = 36
10^a = 6^2
10^(a/2) = 6
log(6) = a/2
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and log(125)=b.
10^b = 125
10^b = 5^3
10^(b/3) = 5
log(5) = b/3
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Find (1/12) in terms of a and b.
1/12 = 5/60 = 5/(6*10)
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log(1/12) = log(5/(6*10)) = log(5)-log(6)-log(10)
= (b/3) - (a/2) - 1
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Cheers,
Stan H.
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