In our first example, the base of the log was 5, and our second example had a base of 4. Now, let’s focus on the notation of logarithms. When we evaluate a logarithmic expression we ask ourselves, “What do I have to raise this base by to get the value of the argument?” Logarithms are the power that is needed. If we rewrite this as a logarithm, we get this: We would say this is a base of 4 raised to the power of 3 is equal to 64. If you’d like to try this out on your own, pause the video and give it a shot! Normally we would say, “five squared equals 25.” If we were to use the terms we used in our first example, we could say, “a base of 5 raised to the power of 2 is equal to 25.” Let’s practice identifying these components and re-writing a few exponential equations as logarithmic equations: This illustrates nicely that logs are the power of a named base. Rearranging these components allows us to write the inverse logarithm, as shown highlighted in green. The answer, 8, is referred to as the argument. The components of an exponential equation are shown here in blue.Ī base of 2 raised to the power of 3 is equal to 8. Let’s get started!īefore we start our work with logarithms, let’s take some time to review the basics of exponential equations. If you want to try some of the examples in this video on your own, grab a scientific calculator and be prepared to practice some skills and explore the power and properties of logarithmic functions. This allows us to use logarithms as a tool to solve exponential equations. In addition, logarithmic functions have an inverse relationship with exponential functions, meaning that they “undo” each other. From sound measured in decibels to the magnitude of earthquakes measured on the Richter Scale, logarithms are used to relate these natural occurrences to a baseline measurement. Hi, and welcome to this review of logarithmic functions! Like all mathematical functions, logarithms are used to measure and model real-life occurrences.
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