Chapter 4 4 5 Exponential and logarithmic equations

Chapter 4 4 -5 Exponential and logarithmic equations

Objectives Solve exponential and logarithmic equations and inequalities. Solve problems involving exponential and logarithmic equations.

Exponential equation O 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#1 O Solve for x O 98 – x = 27 x – 3

Example#2 O Solve for x O 4 x – 1 = 5

Example#3 O Solve O 23 x = 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?

Logarithmic equation O 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#4 O Solve O log (2 x – 1) = – 1 6

Example#5 O Solve O log 100 – log 4(x + 1) = 1 4

Example#6 O Solve O log x 5 4 =8

Student guided practice O Do problems 9 -13 in your book page 270

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

Example#8 O Using a table and graph solve O log(x + 70) = 2 log( x/3 )

Example#9 Use a table and graph to solve 2 x > 4 x – 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.