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title: Basic Log Rules and Expanding Log Expressions
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## Basic Log Rules and Expanding Log Expressions
The following are commonly used basic log rules:
###### Logarithm Product Rule
logb (x * y) = logb (x) + logb (y)
###### Logarithm Quotient Rule
logb (x / y) = logb (x) - logb (y)
###### Logarithm Power Rule
logb (xy) = y * logb (x)
###### Logarithm of Negative Number
logb (x) is undefined when x < 0
###### Logarithm of 0
logb (0) is undefined
limx → 0+ logb (x) = -infinity
###### Logarithm of 1
logb (1) = 0
###### Logarithm of the Base
logb (b) = 1
###### Logarithm of Infinity
lim x → infinity logb (x) = infinity
###### Logarithm Base Switch Rule
logb (c) = 1 / logc (b)
###### Logarithm Base Change Rule
logb (x) = logc (x) / logc (b)
#### More Information:
Logarithm Rules