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In mathematics, there are many logarithmic identities. Logarithms and exponentials with the same base cancel each other.
Logarithms can be used to make calculations easier. For example, two numbers can be multiplied just by using a logarithm table and adding. The laws result from canceling exponentials and appropriate law of indices.
This identity is useful to evaluate logarithms on calculators. 0, but not for large x. The last limit is often summarized as “logarithms grow more slowly than any power or root of x”.