5-6-solving-exponential-and-logarithmic-equations - Objectives 1 Solve exponential and logarithmic equations 2 Solve a variety of application problems

# 5-6-solving-exponential-and-logarithmic-equations -...

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Objectives: 1. Solve exponential and logarithmic equations. 2. Solve a variety of application problems by using exponential and logarithmic equations. Solving Exponential and Logarithmic Equations 5.6 Methods of Solving Exponential Equations 1.Rewrite the bases of the powers on both sides so they are the same. . . Example #1 Powers of the Same Base Solve the equation and confirm your solution with a graph. A. 1 3 9 x x Rewrite both bases to base 3. 1 1 2 3 3 3 3 1 2 1 2 x x x x x x x Example #1 Powers of the Same Base Solve the equation and confirm your solution with a graph. B. 5 3 4 1 2 x x Rewrite to base 2, remember fractions have negative exponents. 10 2 3 5 2 3 5 1 2 3 5 1 3 2 2 2 2 2 2 4 2 x x x x x x x x 3 13 13 3 10 3 3 10 2 3 x x x x x Example #1 continued… Powers of the Same Base Solve the equation and confirm your solution with a graph. C. 625 25 5 2 x x Rewrite to base 5. 1 4 4 5 5 5 5 5 5 5 5 5 5 4 4 4 2 2 4 2 2 4 2 2 x x x x x x x x x Example #1 continued… Powers of the Same Base Solve the equation and confirm your solution with a graph. D. x x 32 2 6 2  1 , 6 0 1 6 0 6 5 5 6 2 2 2 2 2 2 5 6 5 6 2 2 x x x x x x x x x x x x This time the graphs with the intersection method were too difficult to read, so the intercept method was used to verify the two solutions. Example #2 Logarithms on Both Sides Solve the equation. Solutions can be confirmed with a graph. 3 6 x Problems like this can be confusing because students will recognize that 2(3) = 6. Unfortunately, that will not work because we have to be able to rewrite both sides to the same base of a power for the first method to be used. Our only choice then is the second method. 6131 . 0 6 log 3 log 3 log 6 log 3 log 6 log x x x 6131 . 0 6 ln 3 ln 3 ln 6 ln 3 ln 6 ln x x x Notice how common logs and natural logs both work the same way. Choosing which one to use basically comes down to personal preference.   #### You've reached the end of your free preview.

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