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Published byBerenice Murphy Modified over 9 years ago
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7.4 Logarithmic Functions Write equivalent forms for exponential and logarithmic equations. Use the definitions of exponential and logarithmic functions to solve equations. 6.3 Logarithmic Functions
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Rules and Properties Equivalent Exponential and Logarithmic Forms b x = y if and only if x = log b y. 6.3 Logarithmic Functions For any positive base b, where b 1: Exponential formLogarithmic form
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Example 1 a) Write 2 7 = 128 in logarithmic form. 6.3 Logarithmic Functions log 2 128 = 7 b) Write log 6 1296 = 4 in exponential form. 6 4 = 1296
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Rules and Properties What is the inverse of the exponential function y = 10 x ? 6.3 Logarithmic Functions y = log b x is the inverse of y = b x, where b 1 and b > 0. x = 10 y Rewrite x = 10 y in logarithmic form. log 10 x = y So…. Logarithmic Functions
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Rules and Properties 6.3 Logarithmic Functions If b x = b y, then x = y.
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Example 2 a) log 2 1 = r 6.3 Logarithmic Functions Find the value of the variable in each equation: 2 r = 1 2 0 = 1 r = 0
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Simplify the expression a)b)
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Practice 1) log 4 64 6.3 Logarithmic Functions Evaluate each expression 2) log 5 25 3) log 3 243 3 2 5 4) log 1/2 8 -3 5) log 8 8 x x
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Pg. 503 #3-35 odd Homework 6.3 Logarithmic Functions
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