1. 7.4 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

2. 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

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

4. 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

5. Rules and Properties 6.3 Logarithmic Functions If b x = b y, then x = y.

6. Example 2 a) log 2 1 = r 6.3 Logarithmic Functions Find the value of the variable in each equation: 2 r = 1 2 0 = 1 r = 0

7. Simplify the expression a)b)

8. Practice 1) log 4 64 6.3 Logarithmic Functions Evaluate each expression 2) log 5 25 3) log 3 243 3 2 5 4) log 1/2 8 -3 5) log 8 8 x x

9. Pg. 503 #3-35 odd Homework 6.3 Logarithmic Functions