Intro to logarithms (rev1)

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Intro to logarithms (rev1)

  1. 1. Logarithms
  2. 2. ?? ?? LOGARITHM ?? ??
  3. 3. Inverse Functions • Original function: y = kx => f (x) = kx • Inverse function: x x -1 x = ky => y = => f (x) = k k
  4. 4. Example x f (x) = 2x;f (x) = 2 -1
  5. 5. Inverses Invert x g(x) = 2 f (x) = 2x ( æ xö f  g (x) = 2 ç ÷ = x è 2ø ( 2x g  f (x) = =x x ) )
  6. 6. y =k Invert y = k x: x =k y Now solve for y. x
  7. 7. ??????????? ?????????????
  8. 8. Enter the Logarithm () loga b = c means a =b c “Jumping Horse Outline”by warszawianka. Found at http://openclipart.org/detail/10712/jumping-horse-outline-bywarszawianka-10712. Public domain.
  9. 9. x =k Solution: y y = logk x
  10. 10. () loga b = c  a =b c Implications? Graphs of inverse functions reflect over line y = x
  11. 11. Implications • • • • Increasing Asymptote: y-axis => x>0. loga1=0. logaa=1.
  12. 12. Summary Basic relationship: y = a <=> x = loga y x
  13. 13. Next Yes but so what?

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