Introduction to Logarithms Chapter 8.4

Logarithmic Functions log b y = x if and only if b x = y

Rewriting Logarithmic Equations Logarithmic Form log 2 32 = 5 Exponential Form 2 5 = 32 log 5 1 = 0 log = 1 log ½ 2 = = = 10 ( ) -1 = 2 1 2

Special Logarithmic Values Logarithm of 1 log b 1 = 0 because b 0 = 1 Logarithm of Base b log b b = 1 because b 1 = b

Evaluating Logarithmic Expressions Evaluate log to what power gives 81? 3 4 = 81, therefore log 3 81 = 4

The Common Logarithm The logarithm with base 10 is called the common logarithm. It is denoted log 10 or simply log. The log button on your calculator evaluates common logarithms.

Change of Base Formula Let u, b, c be positive numbers b  1 and c , log c u = log b u log b c So to convert expressions to common logarithms in order to use your calculator log c u = log u log c

Properties of Logarithms Let b, u, and v be positive and b  1 Product Property log b uv = log b u + log b v Quotient Property log b = log b u – log b v Power Property log b u n = n log b u uvuv