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The magnitude of an earthquake is a Logarithmic scale. We’ll start off by looking at the exponential function, \[f\left( x \right) = {a^x}\] We want to differentiate this. Where A is the amplitude (in mm) measured by the Seismograph and B is a distance correction factor. We can shift, stretch, compress, and reflect the parent function [latex]y={\mathrm{log}}_{b}\left(x\right)[/latex] without loss of shape.. Graphing a Horizontal Shift of [latex]f\left(x\right)={\mathrm{log}}_{b}\left(x\right)[/latex] For the following, assume that x, y, a, and b are all positive. The famous "Richter Scale" uses this formula: M = log 10 A + B. Logarithmic Functions have some of the properties that allow you to simplify the logarithms when the input is in the form of product, quotient or the value taken to the power. Logarithm Formula for positive and negative numbers as well as 0 are given here. The power rule that we looked at a couple of sections ago won’t work as that required the exponent to be a fixed number and the base to be a variable. That is exactly the opposite from what we’ve got with this function. Note: x > 0 is assumed throughout this article, and the constant of integration is omitted for simplicity. and logarithmic identities here. Some of the properties are listed below. Logarithmic functions are the inverses of exponential functions, and any exponential function can be expressed in logarithmic form. In addition, we discuss how to evaluate some basic logarithms including the use of the change of base formula. All log a rules apply for ln. The following is a list of integrals (antiderivative functions) of logarithmic functions.For a complete list of integral functions, see list of integrals.. Logarithmic Functions Properties. In this section we will introduce logarithm functions. We give the basic properties and graphs of logarithm functions. When a logarithm is written without a base it means common logarithm.. 3. ln x means log e x, where e is about 2.718. We can shift, stretch, compress, and reflect the parent function [latex]y={\mathrm{log}}_{b}\left(x\right)[/latex] without loss of shape.. Graphing a Horizontal Shift of [latex]f\left(x\right)={\mathrm{log}}_{b}\left(x\right)[/latex] Nowadays there are more complicated formulas, but they still use a logarithmic scale. We will also discuss the common logarithm, log(x), and the natural logarithm, ln(x). Product Rule. Sound . Also assume that a ≠ 1, b ≠ 1.. Definitions. Know the values of Log 0, Log 1, etc. Logarithms are really useful in permitting us to work with very large numbers while manipulating numbers of a much more manageable size. 1. log a x = N means that a N = x.. 2. log x means log 10 x.All log a rules apply for log. Similarly, all logarithmic functions can be rewritten in exponential form. 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