Logarithmic functions > Logarithms
12345Logarithms

Theory

Take a look at the applet: Logarithm

The solution of the equation g x = a is called the logarithm of a to base g .
Notation: x = g log ( a ) .

Since this equation only has solutions if 0 < g < 1 or g > 1 and if a > 0 , g log ( a ) can only exist under these conditions.
For the time being you mostly use the intersect function of your graphing calculator to determine x = g log ( a ) .

The general definition for logarithms is:

  • from g x = y follows x = g log ( y ) ;

  • from x = g log ( y ) follows g x = y ;

The expressions x = g log ( y ) en g x = y are completely equivalent if 0 < g < 1 or g > 1 and if y > 0 .
The exponential function and the logarithm with the same base are called inverse operations, since they reverse the effect of each other.

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