College Algebra: Exponential and Logarithmic Functions

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OpenStax — College Algebra 2e

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Linear Adds a fixed amount each period Exponential: multiplies by a fixed factor each period

Example F(x) = log_4(2x - 3) Set 2x - 3 > 0 2x > 3 x > 1.5 Domain: (1.5, infinity)

PARENT FUNCTION CHARACTERISTICS F(x) = log_b(x)

Read it as "log base b of x equals y" means "b raised to y equals x."

Logarithmic to exponential Log_b(x) = y becomes b^y = x

Exponential to logarithmic B^y = x becomes log_b(x) = y

Ask "What exponent do I need on the base to get this number?"

Common logarithm Base 10, written as log(x) with no base shown. Natural logarithm: base e, written as ln(x).