Logarithmic Functions

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Logarithmic Functions
10.2 Logarithmic Functions

• Write equivalent forms for exponential and
  logarithmic equations.
• Use the definitions of exponential and
  logarithmic functions to solve equations.

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Rules and Properties
10.2 Logarithmic Functions

• Equivalent Exponential and Logarithmic Forms

For any positive base b, where b ? 1
bx y if and only if x logb y.
Exponential form
Logarithmic form
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Example 1
6.3 Logarithmic Functions
a) Write 27 128 in logarithmic form.
log2 128 7
b) Write log6 1296 4 in exponential form.
64 1296
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Example 2
6.3 Logarithmic Functions
a. Solve x log2 8 for x.
2x 8
x 3
b. logx 25 2
x2 25
x 5
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Practice
6.3 Logarithmic Functions
c. Solve log2 x 4 for x.
24 x
x 16
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Example 3
6.3 Logarithmic Functions
a. Solve 10x 14.5 for x. Round your answer to
the nearest tenth.
log1014.5 x
x 1.161
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Rules and Properties
6.3 Logarithmic Functions

• What is the inverse of the exponential function y
  10x ?

x 10y
Rewrite x 10y in logarithmic form.
log10x y
So.
Logarithmic Functions
y logb x is the inverse of y bx, where b ?
1 and b gt 0.
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Rules and Properties
6.3 Logarithmic Functions

• One-to-One Property of Exponential Functions

If bx by, then x y.
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Example 4
6.3 Logarithmic Functions
Find the value of the variable in each equation
a) log2 1 r
b) log7 D 3
2r 1
73 D
20 1
D 343
r 0
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Practice
6.3 Logarithmic Functions
Find the value of the variable in each equation
1) log4 64 v
2) logv 25 2
3) 6 log3 v