Collins Type I

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

2. 6.3 Logarithmic Functions 6.3 Logarithmic Functions • Write equivalent forms for exponential and logarithmic equations. • Use the definitions of exponential and logarithmic functions to solve equations.

3. 6.3 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= logby. Exponential form Logarithmic form

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

5. 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

6. 6.3 Logarithmic Functions Practice c. Solve log2x = 4 for x. 24 = x x= 16

7. 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

8. What is the inverse of the exponential function y = 10x ? 6.3 Logarithmic Functions Rules and Properties x = 10y log10x = y Rewrite x = 10y in logarithmic form. So…. Logarithmic Functions y= logbx is the inverse of y = bx, where b 1 and b > 0.

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

10. 6.3 Logarithmic Functions Example 4 Find the value of the variable in each equation: b) log7 D= 3 a) log2 1 = r 73 = D 2r = 1 D = 343 20 = 1 r= 0

11. 6.3 Logarithmic Functions Practice Find the value of the variable in each equation: 1) log4 64 = v 2) logv 25 = 2 3) 6 = log3v

12. More on logarithmic functions and equations Quiz Monday 6.1-6.3 6.3 Logarithmic Functions Homework