10.2 Logarithms and Logarithmic Functions Objectives: 1.Evaluate logarithmic expressions. 2.Solve logarithmic equations and inequalities.

Logarithms The inverse of is In y is called the logarithm of x, usually written read “y equals log base b of x. Logs are a shortcut to solving for x or y. Let b and x be positive numbers, b≠1. The logarithm of x with base b is denoted and it defined as the exponent y that makes the equation true.

Examples Write each equation in exponential form Write each equation in logarithmic form

Logarithmic Functions This function is the inverse of the exponential function It has the following characteristics: 1.The function is continuous and one-to-one. 2.The domain is the set of all positive real numbers. 3.The y-axis is an asmyptote of the graph. 4.The range is the set of all real numbers 5.The graph contains the point (1,0). (The x- intercept is 1)

Properties The following is true for all logarithms: Ex:

Evaluating Log Expressions Write in exponential form. Rewrite with like- bases, set exponents equal to each other. Example: Evaluate:

Logarithmic to Exponential Inequality If b>1, x>0, andthen x> If b>1, x>0, andthen 0<x< If x> If

Property of equality for Log Functions If b is a positive number other than 1, then if and only if x=y. Example: if x=10

Property of Inequality for Log Functions If b>1 then if and only if x>y and if and only if x<y. If then x<8 If then x>3

Examples Solve

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