সপ্তম অধ্যায়ঃ লগরিদম

Submitted by arpita pramanik on Thu, 02/17/2011 - 14:29

সপ্তম অধ্যায়ঃ লগরিদম

 

Properties of Logarithm

1. If   [tex] y = a^x [/tex],   then   [tex] \log_a y = x [/tex].   → Definition of logarithm

2. [tex] \log_a xy = \log_a x + \log_a y [/tex]

3. [tex] \log_a \dfrac{x}{y} = \log_a x - \log_a y [/tex]

4. [tex] \log_a x^n = n \log_a x [/tex]

5. [tex] \log_a a = 1 [/tex]

6. [tex] \log_a 1 = 0 [/tex]

7. [tex] \log_{10} x = \log x [/tex]   →   Common logarithm

8. [tex] \log_e x = \ln x [/tex]   →   Naperian or natural logarithm

9. [tex] \log_y x = \dfrac{\log x}{\log y} = \dfrac{\ln x}{\ln y} [/tex]   →   Change base rule

10. If   [tex] \log_a x = \log_a y [/tex],   then   [tex] x = y [/tex].

11. If   [tex] \log_a x = y [/tex],   then   [tex] x = anti\log_a y [/tex].

 

 

 

 

 

 

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