Daily Warm-UP Quiz 1.Expand: ln x -5 y 2 2x 2. Condense: ½ ln4 + 2 (ln6-ln2) 3. Use properties of logs to solve for x: a. log 81 = x log3 b. log x 8/64 = -3 Answers: 1.) 2 lny – ln2 – 6 lnx 2.) ln 18 3a.) x = 4; 3b.) x = 2

Solving Exponential and Logarithmic Equations Part 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 a 1. log a a x = ___ 2. a log a x = x Base e ln e x = ___ e lnx = x x x

Example 1: Solving an Exponential Equation Solve e x = 72.

Example 2: Solving an Exponential Equation Solve 10 x + 5 = 60.

Example 3: Solving an Exponential Equation Solve 4e 2x = 5

Final Check for Understanding 1. Explain how to solve 2 x = 10 by taking the log of both sides of the equation. Homework Assignment:

Solving Exponential and Logarithmic Equations Part II: During this lesson, you will solve logarithmic equations.

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 = e 3 x = e 3 This procedure is called exponentiating both sides of the equation.

Example 4: Solving a Logarithmic Equation Solve 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 = Pe rt

Final Check for Understanding Explain how to solve log 10 x = 2.4 by exponentiating both sides of the equation. Homework Assignment: