3.4 Exponential and Logarithmic Equations
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1 3.4 Exponential and Logarithmic Equations Pre-Calculus Mr. Niedert Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 1 / 18
2 3.4 Exponential and Logarithmic Equations 1 Solving Simple Equations Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 2 / 18
3 3.4 Exponential and Logarithmic Equations 1 Solving Simple Equations 2 Solving Exponential Equations Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 2 / 18
4 3.4 Exponential and Logarithmic Equations 1 Solving Simple Equations 2 Solving Exponential Equations 3 Solving Logarithmic Equations Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 2 / 18
5 Today s Learning Target(s) 1 I can solve exponential equations. Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 3 / 18
6 Solving Simple Equations You may need to review the following properties as you try to work through the practice problem below. One-to-One Properties a x = a y if and only if x = y log a x = log a y if and only if x = y Inverse Properties a log a x = x log a a x = x Practice Solve the following equations without a calculator. a 2 x = 32 b ln x ln 3 = 0 c ( 1 3) x = 9 d e x = 7 e ln x = 3 f log x = 1 Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 4 / 18
7 Solving Exponential Equations Example Solve each equation and approximate the result to three decimal places if necessary. a e x2 = e 3x 4 b 3 (2 x ) = 42 Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 5 / 18
8 Exact and Approximate Solutions In (b) of the previous example we found an approximate solution of about Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 6 / 18
9 Exact and Approximate Solutions In (b) of the previous example we found an approximate solution of about If you were to find the exact solution then the exact solution is log Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 6 / 18
10 Exact and Approximate Solutions In (b) of the previous example we found an approximate solution of about If you were to find the exact solution then the exact solution is log An exact solution is preferred when the solution is an intermediate step in a larger problem. For a final answer, an approximate solution is easier to comprehend. Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 6 / 18
11 Solving Exponential Equations Practice Solve each equation and approximate the result to three decimal places if necessary. a e x2 = e 5x+6 b 4 (3 x ) = 64 Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 7 / 18
12 Solving Exponential Equations Practice Solve e x + 5 = 60 and approximate the result to three decimal places. Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 8 / 18
13 Solving Exponential Equations Practice Solve 2 ( 3 2t 5) 4 = 11 and approximate the result to the nearest thousandth. Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 9 / 18
14 3.4 Exponential and Logarithmic Equations (Part 1 of 2) Assignment Part 1: pg #1-4, even, EOE Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 10 / 18
15 Today s Learning Target(s) 1 I can solve logarithmic equations. Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 11 / 18
16 Extraneous Solutions When solving logarithmic equations, be sure to check your solution in the original equation. Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 12 / 18
17 Extraneous Solutions When solving logarithmic equations, be sure to check your solution in the original equation. We will need to make sure that the results do not yield extraneous solutions. Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 12 / 18
18 Extraneous Solutions When solving logarithmic equations, be sure to check your solution in the original equation. We will need to make sure that the results do not yield extraneous solutions. Remember that if you end up with extraneous solutions, they are not considered to actually be solutions to the equation. Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 12 / 18
19 Solving Logarithmic Equations Example Solve ln x = 2. Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 13 / 18
20 Solving Logarithmic Equations Practice Solve each equation. a ln x = 2 3 b log 4 (3x + 2) = log 4 (6 x) c log 3 (5x + 13) log 3 6 = log 3 3x Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 14 / 18
21 Solving Logarithmic Equations Practice Solve ln x = 4 and approximate the result to three decimal places. Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 15 / 18
22 Solving Logarithmic Equations Practice Solve 2 log 5 3x = 4. Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 16 / 18
23 Solving Logarithmic Equations Practice Solve log 5x + log(x 1) = 2. Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 17 / 18
24 3.4 Exponential and Logarithmic Equations (Part 2 of 2) Assignment Part 1: pg #1-4, even, EOE Part 2: pg #5-8, EOE 3.4 Exponential and Logarithmic Equations Assignment pg #1-8, even, EOE, EOE Pre-Calculus 3.4 Exponential and Logarithmic Equations Mr. Niedert 18 / 18
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