Log-Functions

# Log-Functions - Logarithmic Functions Logarithmic functions...

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From MathMotivation.com – Permission Granted For Use and Modification For Non-Profit Purposes Logarithmic Functions Logarithmic functions, or for short, log functions, serve as the inverse functions of exponential functions. Why Do We Need Log Functions? If you graph f(x) = 10 X , you get the graph as shown below. We know that this function has an inverse for its entire domain since it passes the horizontal line test. In fact, if we switch x with y, and obtain solution points, we get the graph shown below, which represents a function. Also note the symmetry across the line y=x that is characteristic of a function graphed with its inverse. So we know the inverse of f(x) = 10 X exists, but how do we find it? Using the procedure for finding the inverse, we write y = 10 X switch x with y to get x = 10 y And, now solve for y. But you can’t! So we define y as y = LOG 10 (x), so the inverse of f(x) = 10X is f -1 (x) = LOG 10 (x) which we pronounce as f -1 (x) = the base10 log of x. The BIG result here is that x = 10 y is equivalent to y = LOG 10 (x).

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From MathMotivation.com – Permission Granted For Use and Modification For Non-Profit Purposes Note: You may verify that x = 10 y and y = LOG 10 (x) are equivalent to each other by showing that (x = 100, y=2) and (x=1000, y=3) are solutions for both statements. To
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## This note was uploaded on 11/05/2011 for the course ANTHRO 101 taught by Professor Crandall during the Fall '09 term at BYU.

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Log-Functions - Logarithmic Functions Logarithmic functions...

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