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Warm-Up

Warm-Up. 6.3 Logarithmic Functions. Find the inverse of each function. f(x) = x + 10 g(x) = 3x h(x) = 5x + 3 j(x) = ¼x + 2. 6.3 Logarithmic Functions. 6.3 Logarithmic Functions. Write equivalent forms for exponential and logarithmic equations.

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Warm-Up

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  1. Warm-Up 6.3 Logarithmic Functions Find the inverse of each function. • f(x) = x + 10 • g(x) = 3x • h(x) = 5x + 3 • j(x) = ¼x + 2

  2. 6.3 Logarithmic Functions 6.3 Logarithmic Functions • Write equivalent forms for exponential and logarithmic equations. • Use the definitions of exponential and logarithmic functions to solve equations.

  3. Rules and Properties 6.3 Logarithmic Functions Equivalent Exponential and Logarithmic Forms For any positive base b, where b 1: bx = y if and only if x= logby. Exponential form Logarithmic form

  4. Example 1 6.3 Logarithmic Functions a) Write 27 = 128 in logarithmic form. log2 128 = 7 b) Write log6 1296 = 4in exponential form. 64 = 1296

  5. Example 2 6.3 Logarithmic Functions a. Solve x = log2 8 for x. 2x = 8 x= 3 b. logx 25 = 2 x2 = 25 x= 5

  6. Practice 6.3 Logarithmic Functions c. Solve log2x = 4 for x. 24 = x x= 16

  7. Example 3 6.3 Logarithmic Functions a. Solve 10x = 14.5 for x. Round your answer to the nearest tenth. log1014.5 = x x= 1.161

  8. Rules and Properties 6.3 Logarithmic Functions If bx= by, thenx = y.

  9. Example 4 6.3 Logarithmic Functions Find the value of the variable in each equation: a) log2 1 = r 2r = 1 20 = 1 r= 0

  10. Simplify the expression a) b)

  11. Practice 6.3 Logarithmic Functions Find the value of the variable in each equation: 1) log4 64 = v V=3 V=5 2) logv 25 = 2 3) 6 = log3v V=729

  12. p.436 #30-68 ev Homework 6.3 Logarithmic Functions

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