Logarithms
Monday, July 15, 2013
Logarithms
2:12 PM
A logarithm is essentially an exponent. An expression in
logarithmic form, such as log5125, is read as "log base 5 of 125."
To evaluate log expressions, consider what exponent with a
base of 5 that would equal 125.
An equation in logarithmic form is equivalent to another in
exponential form, as shown below.
Examples:
Basic Logarithm
Rules
Remember that logarithms are closely related to exponents.
Rules for simplifying logarithms are similar to those for
simplifying exponents.
Log Rules can be used to simplify expressions, to expand
expressions, or to solve for values.
Ch. 6 Page 1
If you know the base b logarithm of a number
Logarithm
Change of Base and wish to find its base a logarithm, you can
Formula
use the following formula:
=
Examples:
Find
7
Ch. 6 Page 2
Find
7
Using the change of base formula, letting
b = 10:
7
0.8451
=
= 1.404
4
0.6021
7=
Find
9
9 .9542
=
= 3.170
2 .3010
9=
Find
=
Using
Logarithms to
Solve
Exponential
Equations
!
=
" .#
.$%
= −0.3562
The properties of logarithms help us solve
exponential equations (equations where the
variable occurs in the exponent).
Examples:
Solve 9x=8
9x=8
log 9x=log 8
x log 9 = log 8
x log 9 = log 8
Solve 32x= 5
32x= 5
log 32x= log 5
2x log 3 = log 5
2x log 3 = log 5
Ch. 6 Page 3
2x log 3 = log 5
2x log 3 = log 5
Ch. 6 Page 4