Logarithmic Functions

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Presentation transcript:

Logarithmic Functions Write equivalent forms for exponential and logarithmic equations. Use the definitions of exponential and logarithmic functions to solve equations.

Rules and Properties Equivalent Exponential and Logarithmic Forms 10.2 Logarithmic Functions Rules and Properties Equivalent Exponential and Logarithmic Forms For any positive base b, where b  1: bx = y if and only if x = logb y. Exponential form Logarithmic form

Example 1 a) Write 27 = 128 in logarithmic form. log2 128 = 7 6.3 Logarithmic Functions Example 1 a) Write 27 = 128 in logarithmic form. log2 128 = 7 b) Write log6 1296 = 4 in exponential form. 64 = 1296

Example 2 a. Solve x = log2 8 for x. 2x = 8 x = 3 b. logx 25 = 2 6.3 Logarithmic Functions Example 2 a. Solve x = log2 8 for x. 2x = 8 x = 3 b. logx 25 = 2 x2 = 25 x = 5

Practice c. Solve log2 x = 4 for x. 24 = x x = 16 6.3 Logarithmic Functions Practice c. Solve log2 x = 4 for x. 24 = x x = 16

6.3 Logarithmic Functions Example 3 a. Solve 10x = 14.5 for x. Round your answer to the nearest tenth. log1014.5 = x x = 1.161

Rules and Properties One-to-One Property of Exponential Functions 6.3 Logarithmic Functions Rules and Properties One-to-One Property of Exponential Functions If bx = by, then x = y.

Example 4 Find the value of the variable in each equation: 6.3 Logarithmic Functions Example 4 Find the value of the variable in each equation: a) log2 1 = r b) log7 D= 3 2r = 1 73 = D 20 = 1 D = 343 r = 0

Practice Find the value of the variable in each equation: 6.3 Logarithmic Functions Practice Find the value of the variable in each equation: 1) log4 64 = v 2) logv 25 = 2 3) 6 = log3 v