Base of Logarithm

Example

Reference number:
Consider the number $2$ as the reference number.

Exponent (Power):
Raise it to a power, for example, $5$. In mathematics, this is written as $2^5$ in exponential form.

Result (Quantity):
Now, let’s evaluate it by multiplying the reference number five times.

$\implies$ $2^5$ $\,=\,$ $2 \times 2 \times 2 \times 2 \times 2$

$\,\,\,\,\therefore\,\,\,\,$ $2^5$ $\,=\,$ $32$

Now, let’s understand from this equation that the number $2$ is considered the reference number, and it is raised to the power of $5$ to obtain the number $32$.

Logarithm operation:
The logarithm is a mathematical operation, usually written as “log” in mathematics. It is used to find the exponent to which a reference number must be raised to obtain a given quantity.

$\,\,\,\,\therefore\,\,\,\,$ $\log_{2}{(32)}$ $\,=\,$ $5$

The logarithm of $32$ is $5$ when it is evaluated using $2$ as the reference number. This reference number, $2$, is called the base of the logarithm.