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Showing posts with label Logarithms. Show all posts
Showing posts with label Logarithms. Show all posts

Saturday, 25 February 2012

Logarithms

x = b^y
\therefore \log x = \log b^y
\log x = y \log b
{{\log x} \over {\log b}} = y
\log_b x = y
Therefore,
\text{ if }x = b^y,\text{ then }y = \log_b (x)

Logarithmic Identities

  1. \log_b(xy) = \log_b(x) + \log_b(y)
  2. \log_b\!\left(\begin{matrix}\frac{x}{y}\end{matrix}\right) = \log_b(x) - \log_b(y)
  3. \log_b(x^d) = d \log_b(x)
  4. \log_b\!\left(\!\sqrt[y]{x}\right) = \begin{matrix}\frac{\log_b(x)}{y}\end{matrix}
  5. x^{\log_b(y)} = y^{\log_b(x)}
  6. c\log_b(x)+d\log_b(y) = \log_b(x^c y^d)
  7. \log_b(1) = 0
  8. \log_b(b) = 1
  9. b^{\log_b(x)} = x
  10. \log_b(b^x) = x
  11. \log_a b = {\log_c b \over \log_c a}                                              NEXT
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