Collins Type I What assumption(s) do you make about a population’s growth when you make predictions by using an exponential expression?

6.3 Logarithmic Functions Write equivalent forms for exponential and logarithmic equations. Use the definitions of exponential and logarithmic functions to solve equations. 6.3 Logarithmic Functions

Rules and Properties Equivalent Exponential and Logarithmic Forms b x = y if and only if x = log b y. 6.3 Logarithmic Functions For any positive base b, where b  1: Exponential formLogarithmic form

Example 1 a) Write 2 7 = 128 in logarithmic form. 6.3 Logarithmic Functions log = 7 b) Write log = 4 in exponential form. 6 4 = 1296

Example 2 x = 3 2 x = Logarithmic Functions a. Solve x = log 2 8 for x. x = 5 x 2 = 25 b. log x 25 = 2

Practice x = = x 6.3 Logarithmic Functions c. Solve log 2 x = 4 for x.

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

Rules and Properties What is the inverse of the exponential function y = 10 x ? 6.3 Logarithmic Functions y = log b x is the inverse of y = b x, where b  1 and b > 0. x = 10 y Rewrite x = 10 y in logarithmic form. log 10 x = y So…. Logarithmic Functions

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

Example 4 a) log 2 1 = r 6.3 Logarithmic Functions Find the value of the variable in each equation: 2 r = = 1 r = 0 b) log 7 D= = D D = 343

Practice 1) log 4 64 = v 6.3 Logarithmic Functions Find the value of the variable in each equation: 2) log v 25 = 2 3) 6 = log 3 v

More on logarithmic functions and equations Quiz Monday Homework 6.3 Logarithmic Functions