Properties of Logarithms Keeper 38 Honors Algebra II

Logarithms of Products The Product Rule loga MN = loga M + loga N The logarithm of a product is the sum of the logarithms of the factors

Example Express as a single logarithm:

Logarithms of Powers The Power Rule The logarithm of a power of M is the exponent times the logarithm of M

Example Express as a product.

Example Express as a product.

Example Express as a product.

Logarithms of Quotients The Quotient Rule The logarithm of a quotient is the logarithm of the numerator minus the logarithm of the denominator

Example Express as a difference of logarithms:

Example Express as a single logarithm:

Example – Putting it all together! Express each of the following in terms of sums and differences of logarithms.

Example - Putting it all together! Express each of the following in terms of sums and differences of logarithms.

Example - Putting it all together! Express each of the following in terms of sums and differences of logarithms.

Example - Putting it all together! Express as a single logarithm:

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Expressions of the Type A Base to a Logarithmic Power The number a raised to the power loga x is x

Example Simplify.

Example Simplify.

Example Simplify.