Ch. 8.5 Exponential and Logarithmic Equations

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Objectives Solve exponential and logarithmic equations and equalities.

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Presentation transcript:

Ch. 8.5 Exponential and Logarithmic Equations

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. x = Divide each side by 2 log 5. log 16 2 log 5 0.8614 Use a calculator. Check: 52x 16 52(0.8614) 16 8-5

Check understanding 1

For any positive numbers, M, b, and c, with b ≠ 1, and c ≠ 1, Change of Base Formula For any positive numbers, M, b, and c, with b ≠ 1, and c ≠ 1,

Exponential and Logarithmic Equations ALGEBRA 2 LESSON 8-5 Use the Change of Base Formula to evaluate log6 12. Then convert log6 12 to a logarithm in base 3. log6 12 = Use the Change of Base Formula. log 12 log 6 1.387 Use a calculator. 1.0792 0.7782 log6 12 = log3 x Write an equation. 1.387 log3x Substitute log6 12 = 1.3868 1.387 Use the Change of Base Formula. log x log 3 8-5

Exponential and Logarithmic Equations ALGEBRA 2 LESSON 8-5 (continued) 1.387 • log 3 log x Multiply each side by log 3. 1.387 • 0.4771 log x Use a calculator. 0.6617 log x Simplify. x 100.6617 Write in exponential form. 4.589 Use a calculator. The expression log6 12 is approximately equal to 1.3869, or log3 4.589. 8-5

Check understanding 2

Exponential and Logarithmic Equations ALGEBRA 2 LESSON 8-5 Solve 52x = 120. 52x = 120 log5 52x = log5 120 Take the base-5 logarithm of each side. 2x = log5 120 Simplify. 2x = Use the Change of Base Formula. log 120 log 5 x 1.487 Use a calculator to solve for x. 8-5

Check understanding 3

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

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. log 104 = 4 log 10,000 4 log (2 • 5001 – 2) 4 Check: log (2x – 2) 4 8-5

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

Check understanding 6

Homework P. 464 # 2- 22 even