September 10, 2012
2-5
Logarithmic Functions
Example 1
Write each exponential equation in logarithmic form.
a)
b)
c)
Example 2
Write each logarithmic equation in exponential form.
a)
b)
Example 3
Evaluate each logarithm without using a calculator.
a)
c)
Addition:
Subtraction:
b)
d)
Powers:
Example 4
Use the properties of logarithms to write each expression as a sum,
difference or product of simpler logarithms.
For example:
Change of Base Formula
a)
For example:
b)
In log base 10, we can use our
calculators.
September 10, 2012
Example 5
Example 7
Suppose and
Solve each equation. Round decimal answers to the nearest thousandth.
Use the properties of logarithms to find the following:
a)
b)
Example 6
Use natural logarithms to evaluate each logarithm to the nearest
thousandth.
c)
Example 7
Example 7
Solve each equation. Round decimal answers to the nearest thousandth.
Solve each equation. Round decimal answers to the nearest thousandth.
d)
e)
g)
f)
h)
Example 8
Example 9
Find the domain of the following function.
The number of N(r) since two independently evolving languages split off
from a common ancestral language is approximated by
N(r) = -5000 ln r
where r is the proportion of the words from the ancestral language that
are common to both languages now. Find the following:
a) N(0.9)
b) N(0.5)
c) N(0.3)
d) How many years have elapsed since the split if 70% of the words of
the ancestral language are common to both languages today?
e) If two languages split off from a common ancestral language about
1000 years ago, find r.
September 10, 2012
Example 10
Example 10
The loudness of sounds is measured in a unit called a decibel. To do
this, a very faint sound, called the threshold sound, is assigned an
The loudness of sounds is measured in a unit called a decibel. To do
this, a very faint sound, called the threshold sound, is assigned an
intensity I0. If a particular sound has intensity I, then the decibel rating of
this louder sound is.
intensity I0. If a particular sound has intensity I, then the decibel rating of
this louder sound is.
Find the decibel ratings of the following sounds having intensities as
given. Round answers to the nearest whole number.
Find the decibel ratings of the following sounds having intensities as
given. Round answers to the nearest whole number.
a) Whisper
d) Rock music concert
b) Busy Street
e) Jetliner at takeoff
c) Heavy truck 20 m away