 For positive b and A, b
not equal to 1,
x = log_{b}A means
b ^{x} = A
x is the called the logarithm and A is called the
argument.  Exponential Property of Equality
For positive real numbers b (b not equal to
1)
b ^{x} = b ^{y }
if and only if x = y  Logarithmic Notations
A common logarithm is base 10: log x means log_{10}x
A natural logarithm is base e : ln
x means log_{e}x
 Change of Base Theorem
log_{a}x = log_{b}x / log_{b}A
 The function f defined for positive real numbers
by
f (x) = log_{b}x
where b > 0, b not equal to 1, is called
the logarithmic function with
base b.
 See the directory of curves for the graph
of the logarithmic function
 Properties of Logarithms (Grant's
Tomb Properties)
log_{b}b^{x} = x The
exponent on a base b which is b ^{x}
is x. Duh.. .
b ^{logbx} = x log_{b}x
is the exponent of a base b which gives x.
Double duh.... this is the definition of exponent.
See why these are called Grant's Tomb properties?
 The exponential and logarithmic functions with
base b are inverse functions of one another.
< Back
to Section 5





© 2011 Karl J. Smith. All rights reserved. 