Solve Exponential and Logarithmic Inequalities Vocabulary p An

Solve Exponential and Logarithmic Inequalities

Vocabulary p An exponential inequality in one variable is an inequality that can be written in the form abx + k < 0, abx + k > 0, or abx + k > 0, where a = 0, b > 0, and b = 1. p A logarithmic inequality in one variable is an inequality that can be written in the form logbx + k < 0, logbx + k > 0, or logbx + k > 0, where b > 0, and b = 1.

Solving Exponential and Logarithmic Inequalities… p You can use the same methods used to solve polynomial inequalities in Lesson 2. 4!

Example 1: p Solve 4 x + 1 > 32 n n n Step 1: Write the equation that corresponds to inequality. Step 2: Solve for x. Step 3: plot the x-value on a number line and test intervals [1. 5, ∞)

You Try: 1. Solve the exponential inequality 32 x – 1 < 4 2. 73 x – 4 < 18 p

Example 2: p 1. Solve the logarithmic inequality log 5 x < 2 p p p Step 1: Write the corresponding equation Step 2: solve for x. Step 3: plot the x-value on a number line and test intervals T! U HO C T ues l A a W x-v n the y an lot o m p How d you line? er ul sho numb (0, 25)

Example 2 Cont’d: p 2. Solve the logarithmic inequality log 4 x + 8 > 11 p p p Step 1: Write the corresponding equation Step 2: solve for x. Step 3: plot the x-value on a number line and test intervals [64, ∞)

You Try: 1. Solve the logarithmic inequalities log 62 x + 7 < 10 2. log 9(x – 8) > 3/2 p

Homework: p P. 167 #1 -18