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Rules for Logarithms

​
rule:
definition
log
b
​(b)
log
b
​(1)
log
b
​(x y)
log
b
​​
1
x
​
log
b
​​
x
y
​
log
b
​(​
x
b
​)
log
b
​​
x
y
​
log
a
​(b)
log
a
​(x)
Since
log
b
(x) =
log
b
(
log
a
(x)
a
) =
log
b
(a)
log
a
(x),​it follows that, dividing by
log
b
(a) and switching sides,
log
a
(x) =
log
b
(x)
log
b
(a)
.
The rules for logarithms shown here depend on the laws of exponents and simple algebra. The reason is that the logarithm to the base
b
is the inverse function of
x
b
.
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