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Overview
ALEKS Exponentials and Trigonometry
Logarithmic functions
5. Logarithm rules
5.2 Quotient law of logarithms
Quotient Law of Logarithms
Learn the quotient law of logarithms: log base b of x over y equals log base b of x minus log base b of y, with proof and worked examples.
What You'll Learn
The quotient law of logarithms states that the log of a fraction equals the log of the numerator minus the log of the denominator, as long as the base stays the same.
It comes directly from the exponent rule for dividing powers with the same base.
Applying the law lets you split one hard logarithm into two simpler ones, or combine a subtraction of logs back into a single log.
The rule only works when both logs share the same base and both the numerator and denominator are positive.
A common mistake is trying to apply the quotient law to log of a difference, such as writing log of x minus y as log x minus log y, which is not valid.
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