
These three identities lead to the use of logarithm tables and slide rules; knowing the logarithm of two numbers allows you to multiply and divide them quickly, as well as compute powers and roots.
These are used to solve equations in which the unknowns occur in the exponent.
This identity is needed to evaluate logarithms on calculators. For instance, most calculators have buttons for ln and for log_{10}, but not for log_{2}. To find log_{2}(100), you have to calculate log_{10}(100) / log_{10}(2) (or ln(10)/ln(2), which is the same thing).
The last limit is often summarized as "logarithms grow slower than any power or root of x".
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