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## Converting Between Logarithmic and Exponential Forms

#### High School Functions - HSF-LE.A.4

How to Convert Between Logarithmic and Exponential Forms - Logarithmic and exponential forms are an important part of mathematics. Given that, they are the core concepts used behind the calculation of the magnitudes of the earthquakes. For example, you can compare the magnitudes of two earthquakes, by converting between logarithmic and exponential form. For example, the amount of energy released from the first earthquake was 500 times greater than the energy released from the other. The equation that represents this is the problem is 10x = 500, where x is the difference of magnitude placed on the Richter scale. We have to solve for x. Now, there are different ways to convert them. The first is by using the graphing method. However, estimating from the graphing method can result in an imprecise answer. Thus, we use a log to convert the above exponential function in a logarithmic function. Let's find out practically. First, we have to learn the values of b, y, and x, to write the equation in log form. The b is the base for log form, while x and y are the unknown variables of the function. In the present example 10x = 500, The value of b is 2, while the value of x and y are 3 and 8, respectively. log10⁡ 500 = x. You can use these lessons and worksheets to learn how to transfer values between exponential and logarithmic forms.