1310-Notes-Sec-55

# 1310-Notes-Sec-55 - Solve for x 20 9 2 =-x x e e Example 5...

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Math 1310 Section 5.5 Solving Exponential and Logarithmic Equations Our last topic of the semester will be to solve exponential and logarithmic equations. We’ll start with exponential equations. An exponential equation is an equation in which the variable appears in the exponent. To solve these equations, isolate the exponential expression on one side of the equation, then take the logarithm of both sides of the equation to solve for the variable. You can use either natural logarithms or common logarithms. Read the directions carefully, as they may instruct you as to which to use. Example 1: Solve for x : 9 5 = x . Example 2: Solve for x : 7 5 4 = + x e .

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Example 3 : Solve for x : 10 3 = x Example 4:

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Unformatted text preview: Solve for x : 20 9 2 = +-x x e e . Example 5: Solve for x : 3 2 = +-x e An equation in which the logarithm of the variable occurs is called a logarithmic equation. To solve such an equation, isolate the logarithmic expression on one side of the equation. Then write the equation in exponential form and solve for the variable, or use the law of logarithms to simplify and solve fore the variable. Example 6: Solve for x : 2 ) 4 ( log 3 =-x Example 7: Solve for x : ) 12 ( log ) 5 2 ( log 8 8 = + x Example 8: Solve for x : ) 2 ( log ) 1 ( log log 6 6 6 = + + x x Example 9: Solve for x : 2 ) 5 ( log log 6 6 = + + x x Example 10: Solve for x : ( 29 2 4 ln 2 = + x...
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