7.4 Properties of Logarithms
Name: _________________
Objectives: Students will be able to use the properties of logarithms to
expand and condense logarithmic expressions.
Properties of logs: Let b, m, and n be positive numbers such that b ≠1.
-Product Property: logbmn = logbm + logbn
-Quotient Property: logb(m/n) = logbm - logbn
-Power Property: logbmn = nlogbm
Examples: Use log 43 ≈ 0.792 and log 47 ≈ 1.404 to evaluate the logarithm.
1.) log4(3/7)
2.) log421
Feb 14­7:14 PM
3.) log449
Examples: Expand the expression.
1.) log55x
2.) ln4xy4
3.) log4 5x3
7y
4.) ln∛5x2w
Feb 14­7:19 PM
1
Examples: Condense the expression.
1.) log5x - log5y
2.) 5lnw + ¾lny
3.) logx - logy + 2logz
4.) 2(log320 - log34) + 0.5log34
Feb 14­7:24 PM
Change of Base Formula : If a, b, and c are positive
numbers with b≠1 and c≠1, then: logca = loga
logc
Examples: Use the change-of-base formula to evaluate
the logarithm.
1.) log47
2.) log6(25/4)
Sound Intensity: For a sound with intensity I (in watts per square meter),
the loudness L of the sound (in decibels) is given by the function
L = 10log(I/I0), where I0 is the intensity of a barely audible sound (about
10-12 watts per square meter). Find the decibel level of each:
a.) Barking dog: I = 10-4 W/m2
b.) Bee: I = 10 -6.5 W/m2
Feb 14­7:29 PM
2