5.5 Solving Exponential and Logarithmic Equations Solve exponential equations. Solve logarithmic equations. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

Solving Exponential Equations Equations with variables in the exponents, such as 3x = 20 and 25x = 64, are called exponential equations. Use the following property to solve exponential equations. Like Bases Property For any a > 0, a  1, ax = ay  x = y. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

Example Solve Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

Another Property Property of Logarithmic Equality For any M > 0, N > 0, a > 0, and a  1, loga M = loga N  M = N. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

Examples Solve: e0.08t = 2500. Solve: 3x = 20. Solve: 4x+3 = 3-x. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

Solving Logarithmic Equations Equations containing variables in logarithmic expressions, such as log2 x = 4 and log x + log (x + 3) = 1, are called logarithmic equations. To solve logarithmic equations algebraically, we first try to obtain a single logarithmic expression on one side and then write an equivalent exponential equation. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

Examples Solve: log3 x = 2. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

More Examples Solve: Solve: Copyright © 2012 Pearson Education, Inc.  Publishing as Addison Wesley