Logarithm Rules

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The logarithm of a number to a given base is the power or exponent to which the base must be raised in order to produce that number.

There are four Logarithm rules. They are:-

Product Rule: The logarithm of a product is the sum of the logarithms of the factors.

Quotient Rule: The logarithm of a quotient is the logarithm of the numerator minus the logarithms of the denominator

Power Rule: log_a xⁿ = nlog_a x

Change of base Rule: where x and y are postive, and a > 0, a ≠ 1

Since logarithms are nothing more than exponents, these rules come from the rules of exponents.

The properties of logarithms were very important historically, because they enabled pre-calculator mathematicians to perform multiplication (which is very time-consuming and error prone) by doing addition (which is faster and easier). These rules are still useful in simplifying complicated expressions and solving equations.