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In mathematics, the logarithm is the inverse function to exponentiation. That means that the logarithm of a number x to the base b is the exponent to which b must be raised to produce x. For example, since 1000 = 10 3, the logarithm base of 1000 is 3, or log 10 (1000) = 3.
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 ?
The common logarithm is a logarithm whose base is 10 ("base-10 logarithm"). When writing these logarithms mathematically, we omit the base. It is understood to be 10 .
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.
logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = log b n. For example, 2 3 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log 2 8. In the same fashion, since 10 2 = 100, then 2 = log 10 100.
When you have an equation of the form a^x = b, taking the logarithm of both sides allows you to solve for x. This is particularly useful when dealing with exponential growth or decay problems. Simplifying Complex Calculations: Logarithms can simplify computations, especially when dealing with large numbers or complicated mathematical operations.
Logarithm is another way of writing exponent. The problems that cannot be solved using only exponents can be solved using logs. Learn more about logarithms and rules to work on them in detail.
If you’re ever interested as to why the logarithm rules work, check out my lesson on proofs or justifications of logarithm properties. But if you think you have a good grasp of the concept, you can simply check out the practice problems below to test your knowledge.
Logarithms are the inverses of exponents. They allow us to solve challenging exponential equations, and they are a good excuse to dive deeper into the relationship between a function and its inverse.
Logarithm. A logarithm is the inverse function of exponentiation. A logarithm tells us the power, y, that a base, b, needs to be raised to in order to equal x. This is written as: log b (x) = y
