Math 102 Chapter 6 Test Review

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x=5

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Find the inverse of f(x) = 1/4x - 7

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f^{-1}(x) = 4x + 28

Tags

CCSS.HSF-BF.B.4A

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x=3.5

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3\log x + 7\log y

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Solve using the properties: log_5(x) - log_5(2) = log_5(15)

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x=30

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Definition of an Exponential Function

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A function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent.

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Definition of Logarithm

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The logarithm log_b(a) is the exponent to which the base b must be raised to produce the number a.

Tags

CCSS.HSF.BF.B.5

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Properties of Logarithms: Product Rule

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log_b(mn) = log_b(m) + log_b(n) for any positive m and n.

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Properties of Logarithms: Quotient Rule

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log_b(m/n) = log_b(m) - log_b(n) for any positive m and n.

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Properties of Logarithms: Power Rule

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log_b(m^k) = k * log_b(m) for any positive m and real number k.