Basic rule:
if 23 =8
then log28=3
The logarithm to
the base 2 of 8 is 3
Example
103 = 1000
log101000 = 3
(log = log10 on many calulators)
Rule 1:
logaAB = logaA + logaB
or logaA + logaB = logaAB
Example 1
log102000
=log10(1000x2)
=log101000 + log102
Example 2
log104 + log10250
=log10(4x250)
=log101000
=3
Rule 2:
logn(a/b) = lognA - lognB
or lognA - lognB = logn(a/b)
Example 1
log2(32/2)
=log232 - log22
=5 -1
=4
Example 2
log10500 - log105
=log10(500/5)
=log10100
=2
Rule 3:
lognAm = mlognA
or mlognA=lognAm
Example 1
log525
=log552
=2log55
=2x1
=2
Example 2
log2y3= 6
3log2y = 6
log2y = (6/3)
log2y = 2
y=22
y=4
A brief history of John Napier Examples of Logarithms Answers to Examples
Uses of Logarithms Chemical uses of Logarithms
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