Chapter 4 4-5 Exponential and logarithmic

equations

Objectives

Solve exponential and logarithmic equations and inequalities.

Solve problems involving exponential and logarithmic equations.

Exponential equationO An exponential equation is an

equation containing one or more expressions that have a variable as an exponent.

O To solve exponential equations:•Try writing them so that the bases are all the same.

•Take the logarithm of both sides.

Example#1O Solve for xO 98 – x = 27x – 3

Example#2O Solve for x

O 4x – 1 = 5

Example#3O Solve O 23x = 15

Student guided practice

O Do problems 2 -5 in your book page 270

Biology Application O Suppose a bacteria culture

doubles in size every hour. How many hours will it take for the number of bacteria to exceed 1,000,000?

Logarithmic equationO A logarithmic equation is an

equation with a logarithmic expression that contains a variable. You can solve logarithmic equations by using the properties of logarithms.

Example#4O Solve

O log6(2x – 1) = –1

Example#5O Solve

O log4100 – log4(x + 1) = 1

Example#6O Solve

O log5x 4 = 8

Student guided practice

O Do problems 9 -13 in your book page 270

Example#7O Use a table and graph to solve O 2x + 1 > 8192x.

Example#8O Using a table and graph solve

O log(x + 70) = 2log( x/3 )

Example#9

Use a table and graph to solve 2x > 4x – 1.

Student guided practice

O Do problems 17-19 in your book page 270

Homework O Do even problems from 21-36 in

your book page 270

Closure

Today we saw how to solve exponential and logarithmic functions.Next class we are going to continue with the natural base , e.