1. 5.5 Solving Exponential and Logarithmic Equations
Solve exponential equations.
Solve logarithmic equations.
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2. 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.
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3. Example
Solve
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4. Another Property
Property of Logarithmic Equality For any M > 0, N > 0, a > 0, and a  1, loga M = loga N  M = N.
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5. Examples Solve: e0.08t = 2500. Solve: 3x = 20. Solve: 4x+3 = 3-x.
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6. Solving Logarithmic Equations
Equations containing variables in logarithmic expressions, such as
log2 x = 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.
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7. Examples Solve: log3 x = 2.
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8. More Examples Solve: Solve:
Copyright © 2012 Pearson Education, Inc.  Publishing as Addison Wesley