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Exponential and Logarithmic Equations: Algebra 2 Lesson 8-5

madaline-osborn avatar
madaline-osborn
8 diapositives · 183 Views · Nov 19, 2014

Learn to solve exponential and logarithmic equations in Algebra 2 Lesson 8-5 with step-by-step examples and quick checks. Graph equations, find points of intersection, and solve population decay problems.

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Exponential and Logarithmic Equations: Algebra 2 Lesson 8-5
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  1. Section 8.5 Exponential and Logarithmic Equations

  2. log 16 2 log 5 x = Divide each side by 2 log 5. 0.8614 Use a calculator. Check: 52x 16 52(0.8614) 16 Exponential and Logarithmic Equations ALGEBRA 2 LESSON 8-5 Solve 52x = 16. 52x = 16 log 52x = log 16 Take the common logarithm of each side. 2x log 5 = log 16 Use the power property of logarithms. Quick Check 8-5

  3. Graph the equations y = 43x and y = 1100. Find the point of intersection. The solution is x 1.684 Exponential and Logarithmic Equations ALGEBRA 2 LESSON 8-5 Solve 43x = 1100 by graphing. Quick Check 8-5

  4. Time t 0 1 2 3 4 Pop. P(t) 5000 4000 3201 2561 2049 Step 2: Use the Exp Reg feature to find the exponential function that fits the data. Exponential and Logarithmic Equations ALGEBRA 2 LESSON 8-5 The population of trout in a certain stretch of the Platte River is shown for five consecutive years in the table, where 0 represents the year 1997. If the decay rate remains constant, in the beginning of which year might at most 100 trout remain in this stretch of river? Step 1: Enter the data into your calculator. 8-5

  5. Step 3: Graph the function and the line y = 100. Step 4: Find the point of intersection. The solution is x 18, so there may be only 100 trout remaining in the beginning of the year 2015. Exponential and Logarithmic Equations ALGEBRA 2 LESSON 8-5 (continued) Quick Check 8-5

  6. Check: log (2x– 2) 4 log (2 •5001– 2) 4 log 10,000 4 log 104 = 4 Exponential and Logarithmic Equations ALGEBRA 2 LESSON 8-5 Solve log (2x– 2) = 4. log (2x– 2) = 4 2x– 2 = 104 Write in exponential form. 2x– 2 = 10000 x = 5001 Solve for x. Quick Check 8-5

  7. x3 2 Log ( ) = 5 Write as a single logarithm. x3 2 = 105 Write in exponential form. 3 x = 10 200, or about 58.48. 3 The solution is 10 200, or about 58.48. Exponential and Logarithmic Equations ALGEBRA 2 LESSON 8-5 Solve 3 log x– log 2 = 5. 3 log x– log 2 = 5 x3 = 2(100,000) Multiply each side by 2. Quick Check 8-5

  8. 1 8 Exponential and Logarithmic Equations ALGEBRA 2 LESSON 8-5 Use mental math to solve each equation. 1. 2x = 2. log42 = x3. 106x = 1 4. Solve 52x = 125. 1 2 –3 0 3 2 8-5