Examples: a) log2 8 = 3 b) log4 2 = 1/2 c) log1/2 16 = 4 d) log7 1 = 0

Unit 8: Logarithmic Functions (8.4) p.486492
Definition of Logarithm with base b:
Let b and y be positive #'s, b≠1. The logarithm of y with base b denoted by logb y is defined as:
logb y = x if and only if bx = y
Examples: a) log2 8 = 3
c) log1/2 16 = 4
b) log4 2 = 1/2
d) log7 1 = 0
1
Special Logarithm Values
Log of 1
logb 1 = 0
Log of Base b
logb b = 1 2
Ex 1: Evaluate the expression
a) log4 64
b) log2 32 c) log5 125
d) log16 2
e) log1/3 27
f) log4 .25
3
Logarithm with base 10 is the common logarithm
log10 x = log x
Logarithm with base e is the natural logarithm
loge x = ln x
Examples: a)
log 7
b) ln .4
4
Inverse Log Functions
g(x) = logb x is the inverse of f(x) = bx
b = x
f(g(x)) = blog x
g(f(x)) = logb bx = x
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Ex 2: simplify
a) 10log 5
c) log4 16x
4
b) 4log 7
d) log3 27x
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Ex 3: Find the inverse of the function
a) y = log5 x
c) y = ln (x 3)
b) y = log x
d) y = ln (2x + 4)
7
Graphs of Logarithmic Functions
y = logb (x h) + k
x = h is a vertical asymptote
x > h is the domain, and range is all real numbers
if b>1 the graph moves up to the right
if 0<b<1 the graph moves down to the right
8
Ex 4: Graph. State the domain and range.
a) y = log2 x + 1
b) y = log3 (x 2)
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HW: p.490491
#1638 even
#4872 even
#79, 80
10

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