3.3 PROPERTIES OF LOGARITHMS - Utep

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Transcript of 3.3 PROPERTIES OF LOGARITHMS - Utep

Slide 12
evaluate logarithmic expressions.
rewrite logarithmic expressions.
condense logarithmic expressions.
real-life problems.
a.
b.
Example 3 – Using Properties of Logarithms
Write each logarithm in terms of ln 2 and ln 3.
a. ln 6 b. ln
Solution:
= ln 2 + ln 3
= ln 2 – ln 33
Product Property
Power Property
Find the exact value of each expression without using a
calculator.
= log5 5 1 3 =
= 6 ln − 2 ln = 6 − 2 = 4
= ln 6
2 = ln 6−2 = ln 4 = 4 ln = 4
10
Expand each logarithmic expression.
a. log4 5x3y = log4 5 + log4 x 3 + log4 y
= log4 5 + 3 log4 x + log4 y
Product Property
Power Property
= log 1 2 + log + 1 3
= log 1 2 + 1 3
= log + 1 3
14
Continue…
= ln + 2 2
= 1
= log2 ( + 1) 3
16
Application
17
Application
If the points are graphed and fall on a line, then you can
determine that the x- and y-values are related by the
equation
where m is the slope of the line.
18
19
Y= 3
2 X, where Y = ln x and X = ln x
ln = 3
2 ln