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Warm-Up. 6.3 Logarithmic Functions. Find the inverse of each function. f(x) = x + 10 g(x) = 3x h(x) = 5x + 3 j(x) = ¼x + 2. 6.3 Logarithmic Functions. 6.3 Logarithmic Functions. Write equivalent forms for exponential and logarithmic equations. - PowerPoint PPT Presentation
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Warm-Up
Find the inverse of each function.
1) f(x) = x + 10
2) g(x) = 3x
3) h(x) = 5x + 3
4) j(x) = ¼x + 2
6.3 Logarithmic Functions
6.3 Logarithmic Functions
• Write equivalent forms for exponential and logarithmic equations.
• Use the definitions of exponential and logarithmic functions to solve equations.
6.3 Logarithmic Functions
Rules and Properties
Equivalent Exponential and Logarithmic Forms
310 1000
bx = y if and only if x = logb y.
6.3 Logarithmic Functions
For any positive base b, where b 1:
Exponential form Logarithmic form
10 1log 000 3
Example 1
a) Write 27 = 128 in logarithmic form.
6.3 Logarithmic Functions
log2 128 = 7
b) Write log6 1296 = 4 in exponential form.
64 = 1296
Example 2
x = 3
2x = 8
6.3 Logarithmic Functions
a. Solve x = log2 8 for x.
x = 5
x2 = 25
b. logx 25 = 2
Practice
x = 16
24 = x
6.3 Logarithmic Functions
c. Solve log2 x = 4 for x.
Example 3
x = 1.161
log1014.5 = x
6.3 Logarithmic Functions
a. Solve 10x = 14.5 for x. Round your answer to the nearest tenth.
Rules and Properties
logb xb xlog x
b b x
log 1 0b
6.3 Logarithmic Functions
If bx = by, then x = y.
log 1b b
Example 4
a) log2 1 = r
6.3 Logarithmic Functions
Find the value of the variable in each equation:
2r = 1
20 = 1r = 0
Simplify the expression
a)2log 2x
x
7log 37 xb)
3x
Practice
1) log4 64 = v
6.3 Logarithmic Functions
Find the value of the variable in each equation:
2) logv 25 = 2
3) 6 = log3 v
V=3
V=5
V=729
p.436 #30-68 ev
Homework6.3 Logarithmic Functions