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Ch. 8.3 Logarithmic Functions as Inverses

Ch. 8.3 Logarithmic Functions as Inverses. E • 30 6 E • 30 3. Write a ratio. 30 6 30 3. = Simplify. Logarithmic Functions as Inverses. ALGEBRA 2 LESSON 8-3. Compare the amount of energy released in an earthquake that registers 6 on the Richter scale with one that registers 3.

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Ch. 8.3 Logarithmic Functions as Inverses

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  1. Ch. 8.3 Logarithmic Functions as Inverses

  2. E • 306 E • 303 Write a ratio. 306 303 = Simplify. Logarithmic Functions as Inverses ALGEBRA 2 LESSON 8-3 Compare the amount of energy released in an earthquake that registers 6 on the Richter scale with one that registers 3. = 306–3Division Property of Exponents = 303Simplify. = 27,000 Use a calculator. The first earthquake released about 27,000 times as much energy as the second. 8-3

  3. Logarithm • The logarithm to the base of a positive number y is defined as follows: If , then

  4. Logarithmic Functions as Inverses ALGEBRA 2 LESSON 8-3 Write: 32 = 25 in logarithmic form. If y = bx, then logby = x. Write the definition. If 32 = 25, then log232 = 5. Substitute. The logarithmic form of 32 = 25 is log2 32 = 5. 8-3

  5. Check Understanding • P. 439 #2 A - C

  6. Logarithmic Functions as Inverses ALGEBRA 2 LESSON 8-3 Evaluate log3 81. Let log3 81 = x. Log381 = xWrite in logarithmic form. 81 = 3xConvert to exponential form. 34 = 3x Write each side using base 3. 4 = xSet the exponents equal to each other. So log3 81 = 4. 8-3

  7. p. 439 Check understanding 3 A - C

  8. A common logarithm is a logarithm that uses base 10. You can write the common logarithm as log y

  9. Logarithmic Function

  10. Step 1: Graph y = 4x. Step 2: Draw y = x. Step 3: Choose a few points on 4x. Reverse the coordinates and plot the points of y = log4x. Logarithmic Functions as Inverses ALGEBRA 2 LESSON 8-3 Graph y = log4x. By definition of logarithm, y = log4x is the inverse of y = 4x. 8-3

  11. Step 2: Graph the function by shifting the points from the table to the right 1 unit and up 2 units. x y = log5x –3 1 25 –2 1 125 –1 0 1 1 5 5 1 Logarithmic Functions as Inverses ALGEBRA 2 LESSON 8-3 Graph y = log5 (x – 1) + 2. Step 1: Make a table of values for the parent function. 8-3

  12. Homework • Page 441, #6 – 22 eoe, 36 – 40 even

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