Logarithms

What is it?

A logarithm is a mathematical concept that can be expressed as the exponential relationship between numbers. Basically, the logarithm of a number is the exponent at which should we elevate the base number until results in the number itself.

So, ${\log }_{2}8=3$, because $2^3=8$.

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Logarithmic specifics

There are two specific logarithms, which have their own names:

• $lo{g}_e$ is called the natural logarithm, written as $\ln$.

• $lo{g}_{10}$ is called the common logarithm, written with no base, only as $\log$.

Apart from that, there are also some logarithm properties that can help to calculate some equations:

• ${\log }_{c}1=0$

• $lo{g}_{c}c=1$

• ${\log }_c(\frac{a}{b})={\log }_{c}a-{\log }_{c}b$

• ${\log }_c{a}^b=b\ast {\log }_{c}a$

• $lo{g}_{a}b=\frac{{\log }_{c}b}{{\log }_{c}a}$

• $lo{g}_a{a}^b=b$

• $a^{{\log }_{a}b}=b$

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Logarithm function

A logarithm function is the inverse of an exponential function. You can transform an exponential function into a logarithm one and they would mirror each other:

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