Question 1202165: Determine the appropriate base of each logarithm
log base b (1/15)=-1.9
log base b 80=3.9
log base b 6=0.9
log base b 66=3.1
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Determine the appropriate base of each logarithm
log base b (1/15)=-1.9
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---> b^-1.9 = 1/15
Solve for b
Using ln, natural logs, base e:
-1.9*ln(b) = ln(1/15)
ln(b) = ln(1/15)/(-1.9)
ln(b) = -2.708/(-1.9) = ~1.4252
b = e^(1.4252)
b =~ 4.159
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log base b 80=3.9
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b^3.9 = 80
Using common logs, base 10:
3.9*log(b) = log(80)
log(b) = log(80)/3.9 = ~0.48797
b = 10^(0.48797) = ~3.0759
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log base b 6=0.9
log base b 66=3.1
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