Lesson23

# Lesson23 - Summer MA 15200 Lesson 23 Section 4.4 An...

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1 Summer MA 15200 Lesson 23, Section 4.4 An exponential equation is an equation with a variable in one of its exponents. A logarithmic equation is an equation with one or more logarithmic expressions that contain a variable. Solving an exponential equations: A If you can write the left and right sides using the same base, then the exponents are the same. For example: () () 35 1 1 34 94 ( 5 1 ) 81 6 22 92 04 41 1 4 11 xx x x x x = = = =− = = This cannot always be done, however. If two quantities are equal, the logs to the same base of those quantities are equal. Therefore: log log bb M NM N =⇔ = B Therefore, to solve an exponential equation: 1. Write with exponential expression on one side. 2. Take either the common logs or the natural logs of both sides. 3. Use the properties of logs and solve. 4. Use a scientific calculator if asked to approximate. Ex 1: Solve each equation. Approximate to 4 decimal places, if necessary. 2 2 1 ) 8 2 3 3 x x ab −− == 9 13 x c = If , then MN M N = = If possible, try to write both exponential expression with the same base.

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Lesson23 - Summer MA 15200 Lesson 23 Section 4.4 An...

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