Properties of Logarithm

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Properties of Logarithms

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Presentation transcript:

Properties of Logarithm Logarithmic Funcitons

Review: Evaluating exponents

loga x = y a y = x Logarithims A logarithmic function is the inverse function of an exponential function. loga x = y a y = x

loga x = y log2 8 = 3 Read as : “logarithm of x with base a equals y” “logarithm of 8 with base 2 equals 3”

Logarithms Convert each of the following to a logarithmic equation. Convert each of the following to a exponential Function: a) log2 4 = m b) log5 w = 9 59 = w 2m = 4 Convert each of the following to a logarithmic equation. a) 25 = 5x b) ew = 30 log5 25 = x loge 30 = w

Evaluating Logarithms Example1: log5 x = 2 5 2= x Change the logarithmic to exponential function: log5 x = 2 25 = x

Evaluating Logarithms Example1: logb 64 = 3 b 3= 64 Change the logarithmic to exponential function: logb 64 = 3 b = 4

Evaluating Logarithms Example1: log3 7 = y 3 y= 7 Change the logarithmic to exponential function: log3 7 = y

Equivalent Exponential Equation Examples: Write the equivalent exponential equation and solve for y. Solution Equivalent Exponential Equation Logarithmic Equation y = log216 16 = 2y y = 4 y = log2( ) = 2 y y = –1 9 y = log416 16 = 4y y = 2 y = log51 1 = 5 y y = 0