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Logarithms Section 4(3)

Logarithms Section 4(3). 2x = 8 is solved using division (inverse of multiplication). To solve equations we use inverse operations. x – 5 = 9 is solved using addition (inverse of subtraction). Now . . . we need an inverse to solve: 5 x = 8.

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Logarithms Section 4(3)

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  1. LogarithmsSection 4(3)

  2. 2x = 8 is solved using division (inverse of multiplication) To solve equations we use inverse operations x – 5 = 9 is solved using addition (inverse of subtraction) Now . . . we need an inverse to solve: 5x = 8

  3. Log Definition: Exponent form: 5x = 8 Log form: Log5 8 = x

  4. Practice: • Exponent Log • form: form: • 3x = 7 • 2) Log2 6 = w • 4x = 16 • Log3 x = 5 Log3 7 = x 2w = 6 Log4 16 = x 35 = x

  5. Properties: • Loga 1 = 0 2) Loga ax = x 3) If Log x = Log y then x = y 4)

  6. Definitions: Base 10 Log: Log10 x = Log x We don’t write the 10 Natural Log: Loge x = Ln x and e = 2.7182818…

  7. Evaluate Each: Make into Powers = Power 3 1) Log2 8 2) Log4 256 4 -2 9

  8. Solve Each: Write as Exponents first x = +5 x = 32 x = 3/2

  9. Graphing Logs This is the inverse of the exponential function: Re-write Exchange x & y Domain Range

  10. LogarithmProperties

  11. Change Bases:

  12. Product: Loga xy = Loga x + Loga y Quotient: Loga x/y = Loga x - Loga y Power: Loga xy = y Loga x

  13. Expand each • Log3 5x = • Log 7/3 = • 3) Ln 53 = Log3 5 + Log3 x Log 7 - Log 3 3 Ln 5

  14. Expand Each

  15. Condense

  16. Ch 4 Section 4Using a Calculator

  17. Findeach: Below “x” represents the number of years since 1900 and the answer is a percent. What is the percent for 1995?

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