Daily Warm-UP Quiz

1. Expand: ln x -5 y2

2x

2. Condense: ½ ln4 + 2 (ln6-ln2)

3. Use properties of logs to solve for x: a. log 81 = x log3 b. logx 8/64 = -3Answers: 1.) 2 lny – ln2 – 6 lnx 2.) ln 18 3a.) x = 4; 3b.) x = 2

Solving Exponential and Logarithmic

EquationsPart I: During this lesson, you will solve exponential equations.

Inverse Properties of Exponents and Logarithms

Let a be a positive real number; a ≠ 1.

Base a1. loga ax = ___

2. alogax = x

Base eln ex = ___e lnx = x

xx xx

Example 1: Solving an Exponential Equation

Solve ex = 72.

Example 2: Solving an Exponential Equation

Solve 10x + 5 = 60.

Example 3: Solving an Exponential Equation

Solve 4e 2x = 5

Final Check for Understanding

1. Explain how to solve 2x = 10 by taking the log of both sides of the equation.

Homework Assignment:

Daily Warm-UP Quiz

1. What are two ways to determine if an equation is an exponential equation?

2. Describe the step-by-step procedure for solving an exponential equation.

3. Use Properties of Logs Properties of Logs to solve for x:

logx 27/64= 3

4. Expand the expression: (2x/x2)3

Solving Exponential and Logarithmic

EquationsPart II: During this lesson, you will solve logarithmic

equations.

Before we start recall Inverse Properties of Exponents and Logarithms:

Solving Logarithmic Equations

NOTE: To solve a logarithmic equation such as

ln x = 3, we write the equation in exponential form as follows:

e ln x = e3

x = e3

This procedure is called exponentiating both sides of the equation.

Example 4: Solving a Logarithmic Equation

Solve 5 + 2 ln x = 4.

Example 5: Solving a Logarithmic Equation

Solve 2 log 10 3x = 4.

Example 6: Doubling Time

You have deposited $500 in an account that pays 6.75% interest, compounded continuously. How long will it take for your money to double?A = ____; P = ____; r = ____ t = ___

A = Pert

Final Check for Understanding

Explain how to solve log 10 x = 2.4 by exponentiating both sides of the equation.

Homework Assignment: