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MAT_1143-mar_30 - Click to edit Master subtitle style...

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Click to edit Master subtitle style March 30, 2011 Sections 4.7
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Exact Answer Rule of 70 gave us approximate answer to 2 = ax For the EXACT answer, we need to introduce a new function that reverses the role of input and output on the exponential This is not the first time we have done this We have done exponential versus radical form to solve for the base in some exponentials 32 = 9, so A:31/2=9 B: 91/2 = 3 C: (1/2)3 = 9 D: (1/2)9 = 3
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Exact Answer x2 = 11, so x = A: 121 B: 5.5 C. sqrt(11) D. 11 We are used to using a new function (and the calculator to compute it if we don’t know it exactly) with the square root Section 4.7 introduces another new function-the logarithm- and 6.1 on continues to use it.
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Logarithm Our new function is the logarithm function loga x = y means ay = x We HAVE to get comfortable with this concept And going from logarthmic to exponential form and vice versa. The logarithm is giving us an exponent It is the exponent that is used to give the input x to the logarithm function Note the base a is the same in each Inputs/Outputs are reversed
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