logarithmic functions section 2. objectives change exponential expressions to logarithmic...
TRANSCRIPT
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Logarithmic Functions
Section 2
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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
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where a > 0 and a ≠ 1
Domain: x > 0€
y = loga x if and only if x = ay
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Change to an equivalent logarithmic function
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1.23 = m
eb = 9
a4 = 24
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Change to an equivalent exponential function
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loga 4 = 5
loge b = −3
log3 5 = c
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Find the exact value of the logarithmic expression
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log216
log3
1
27
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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
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Find the domain of the logarithmic function
€
f (x) = log2(x + 3)
g(x) = log5
1+ x
1− x
⎛
⎝ ⎜
⎞
⎠ ⎟
h(x) = log1
2
x
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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
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y = ln x if and only if x = ey
(inverse functions)
========================
y = log x if and only if x = 10y
(inverse functions)
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Solve the logarithmic equation.
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log3(4x − 7) = 2
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Solve the logarithmic equation.
€
logx 64 = 2
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Use a logarithm to solve the equation.
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e2x = 5
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Pages 515-516 (22-56 even)
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Pages 517-518 (76-110 even, 118, 121)