Logarithm

Part of mathematics. They are related to exponential functions. A logarithm tells what exponent (or power) is needed to make a certain number, so logarithms are the inverse of exponentiation. Historically, they were useful in multiplying or dividing large numbers. - Simple English Wikipedia

Logarithms are the inverse operation of exponentiation. We can use logarithms to find the exponent, to which a given base number must be raised in order to produce a particular result.
- Khan Academy

Logarithm it’s inverse of exponents.

$l o g_{2} (1024)$ means, I need to get a number X, where $2^{X} = 1024$ , and result is == $10$ ==. Here $2^{10}$ is exponent and $l o g_{2} (1024)$ is inverse of exponent.

One method of finding logarithm is dividing number until we get a 1 as result, for example, how to find $l o g_{2} (2048)$ with this method?
How many times need to divide 2 to get 1 as result $2048 \div 2 \div 2 \div 2 \div 2 \div 2 \div 2 \div 2 \div 2 \div 2 \div 2 \div 2 = 1$ . So answer is 11.

In computer science, unlike in math when we’re saying $O (lo g N)$ , we actually shorthand for saying == $O (lo g_{2} N)$ ==.

References

How logarithms interconnect with powers and exponents?
Introduction to Logarithms

Inom Turdikulov

Logarithm

References

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