1 Aralık 2013 Pazar

Propertıes of Logarithms
  • \log_b(x y) = \log_b (x) + \log_b (y) \,
  • \log_b \!\left(\frac x y \right) = \log_b (x) - \log_b (y) \,
  • \log_b(x^p) = p \log_b (x) \,
  • \log_b \sqrt[p]{x} = \frac {\log_b (x)} p \,

The logarithm of a product is the sum of the logarithms of the numbers being multiplied; the logarithm of the ratio of two numbers is the difference of the logarithms. The logarithm of the p-th power of a number is p times the logarithm of the number itself; the logarithm of a p-th root is the logarithm of the number divided by p.

Change of Base

The logarithm logb(x) can be computed from the logarithms of x and b with respect to an arbitrary base k using the following formula:
\log_b(x) = \frac{\log_k(x)}{\log_k(b)}.\,
Typical scientific calculators calculate the logarithms to bases 10 and e.Logarithms with respect to
any base b can be determined using either of these two logarithms
 by the previous formula : 

\log_b (x) = \frac{\log_{10} (x)}{\log_{10} (b)} = \frac{\log_{e} (x)}{\log_{e} (b)}. \,









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