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Logarithm

Logarithm. By: Riry Sriningsih, S.Si., M.Sc. Fridgo Tasman, S.Pd., M.Sc . Logarithm . Logarithm is an invers of exponent. Therefore between logarithm and exponent have relation as follow: a x = b then x = a log b, where b>0, a>0 and a ≠ 1 a is base of logarithm b is numerous

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Logarithm

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  1. Logarithm By: Riry Sriningsih, S.Si., M.Sc. Fridgo Tasman, S.Pd., M.Sc.

  2. Logarithm Logarithm is an invers of exponent. Therefore between logarithm and exponent have relation as follow: ax = b then x = a log b, where b>0, a>0 and a ≠ 1 a is base of logarithm b is numerous x is the result of logarithm

  3. Properties of Logarithm There are some properties of logarithm • a log a = 1 • log a . b = log a + log b • log a/b = log a – log b • a log b . b log c = a log c • log an = n log a • a log x = log x / log a • a log x = 1 / x log a

  4. Properties of Logarithm Example : Simplify the equation below: a log b . c log d . b log c

  5. Properties of logarithm By using the properties number four on previous slide we can answer that question. First we have to transform the problem into a log b . b log c . c log d Using the properties number four we can simplify that problem into a log d

  6. Properties of Logarithm Determine the value of a log 1/b . b log 1/c2 . c log 1/a3 ?

  7. Exercise By using the properties of logarithm answer the problem below: • If log a2 / b2= 12 then determine the logarithm of the cube root of b/a? • Count the value of log (1/5 square root of 15), if log 3=a and log 5 = b ? • If 7 log 2 = a and 2 log 3 = b, determine the value of 6 log 98 in a and b? • Determine the natural numbers that satisfy the inequalities 8 log (x2 – 2x) < 1

  8. Logarithm function Logarithm function denote as y = a log x, where x>1, a>0 and a ≠ 0 Logarithm function is an invers of exponential function. Therefore the graph of logarithm function is a symmetry of exponential function where a symmetry line is y=x

  9. Can you draw the graph of 10 log (x2 + 3x + 3) ?

  10. Thanks for your attention

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