Chapter 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 9 8 – x = 27 x – 3

Example#2 O Solve for x O 4 x – 1 = 5

Example#3 O Solve O 2 3x = 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 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 6 (2x – 1) = –1

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

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

Student guided practice O Do problems in your book page 270

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

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

Example#9 Use a table and graph to solve 2 x > 4 x – 1.

Student guided practice O Do problems in your book page 270

Homework O Do even problems from 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.