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27 Αυγ 2020 · Definition. A logarithm is the answer to the question what power x do I need to apply to the base b in order to obtain the number y: log_b(y) = x is another way of specifying the relationship: b^x = y. Let’s plug in some numbers to make this more clear. We will do base-10, so b=10.
So, why do logarithmic functions exist? It is because exponential functions are one-to-one. Whether you want to use logarithms or not they exist because a bijective function has an inverse.
Introduction to Logarithms. In its simplest form, a logarithm answers the question: How many of one number multiply together to make another number? Example: How many 2 s multiply together to make 8? Answer: 2 × 2 × 2 = 8, so we had to multiply 3 of the 2 s to get 8. So the logarithm is 3. How to Write it. We write it like this: log2(8) = 3.
Evaluating Logarithms. Evaluating logarithms is one of the funnest things to do with logarithms. For example, if you have. log28, you can set it equal to x. log28 = x, then rewrite it in exponential form as. 2x = 8, then rewrite it as.
In this article, we are going to learn the definition of logarithms, two types of logarithms such as common logarithm and natural logarithm, and different properties of logarithms with many solved examples.
Logarithms are inverse functions (backwards), and logs represent exponents (concept), and taking logs is the undoing of exponentials (backwards and a concept). And this is a lot to take in all at once.
Logarithms are defined as the solutions to exponential equations and so are practically useful in any situation where one needs to solve such equations (such as finding how long it will take for a population to double or for a bank balance to reach a given value with compound interest).
