- For positive b and A, b
not equal to 1,
x = logbA means
b x = A
x is the called the logarithm and A is called the
- Exponential Property of Equality
For positive real numbers b (b not equal to
b x = b y
if and only if x = y
- Logarithmic Notations
A common logarithm is base 10: log x means log10x
A natural logarithm is base e : ln
x means logex
- Change of Base Theorem
logax = logbx / logbA
- The function f defined for positive real numbers
f (x) = logbx
where b > 0, b not equal to 1, is called
the logarithmic function with
- See the directory of curves for the graph
of the logarithmic function
- Properties of Logarithms (Grant's
logbbx = x The
exponent on a base b which is b x
is x. Duh.. .
b logbx = x logbx
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.
to Section 5
© 2011 Karl J. Smith. All rights reserved.