logarithmic functions section 2. objectives change exponential expressions to logarithmic...
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Logarithmic Functions
Section 2
Objectives
• Change Exponential Expressions to Logarithmic Expressions and Logarithmic Expressions to Exponential Expressions
• Evaluate Logarithmic Expressions • Determine the Domain of a Logarithmic
Function• Graph Logarithmic Functions• Solve Logarithmic Equations
where a > 0 and a ≠ 1
Domain: x > 0€
y = loga x if and only if x = ay
Change to an equivalent logarithmic function
€
1.23 = m
eb = 9
a4 = 24
Change to an equivalent exponential function
€
loga 4 = 5
loge b = −3
log3 5 = c
Find the exact value of the logarithmic expression
€
log216
log3
1
27
Since logarithmic and exponential functions are inverses of each other,
Domain of the logarithmic fx. = Range of the exponential fx. = (0, ∞)
Range of the logarithmic fx. = Domain of the exponential fx. = (-∞, ∞)
The argument of a logarithmic function must be greater than zero
Find the domain of the logarithmic function
€
f (x) = log2(x + 3)
g(x) = log5
1+ x
1− x
⎛
⎝ ⎜
⎞
⎠ ⎟
h(x) = log1
2
x
Properties of the Logarithmic Function f(x) = logax
• Domain: Positive reals Range: All reals• x-intercept: 1 y-intercept: None• y-axis is a vertical asymptote• Decreasing if 0 < a < 1 and increasing if a > 1• Graph contains the points (1, 0), (a, 1), and
(1/a, -1)• Graph is smooth and continuous, with no corners
or gaps
y = ln x if and only if x = ey
(inverse functions)
========================
y = log x if and only if x = 10y
(inverse functions)
Solve the logarithmic equation.
€
log3(4x − 7) = 2
Solve the logarithmic equation.
€
logx 64 = 2
Use a logarithm to solve the equation.
€
e2x = 5
Pages 515-516 (22-56 even)
========================
Pages 517-518 (76-110 even, 118, 121)
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