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Lesson31

# Lesson31 - MA 15200 Lesson 31 Section 4.4 An exponential...

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1 MA 15200 Lesson 31, 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: (There are 2 types of exponential equations.) A If you can write the left and right sides using the same base, then the exponents are the same. For example: ( ) ( ) 3 5 1 3 5 1 3 4 9 4(5 1) 8 16 2 2 2 2 9 20 4 4 11 4 11 x x x x x x 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 b b M N M 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.

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Lesson31 - MA 15200 Lesson 31 Section 4.4 An exponential...

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