Section 5.3 Properties of Logarithms Advanced Algebra

Properties of Logarithms log b 1 = 0 Anything raised to the 0 power is 1. log b b = 1 Anything raised to the 1st power is that anything log b b x = x Think about as exponent: b x = b x Rewrite as a log: log b x = log b x

Common and Natural Log Properties log 1 = 0 log 10 = 1 log 10 x = x 10 log x = x x > 0 ln 1 = 0 ln e = 1 ln e x = x e ln x = x if x > 0

Simplifying

Simplify Using Properties

More Simplifying

3 More Properties Product Rule log b MN = log b M + log b N Quotient Rule Power Rule

Write as a sum or difference of logs

Expand as a sum and difference of logs

Expand the log into a sum or difference of logs

Write the difference as a single log

Write the sum as a single log To use the product or quotient rules of logs, remember, the bases must be the same.

Combine into a single log

Condense to a single logarithm

Evaluate log 4 5 Change of Base Formula

Evaluate