To solve logarithms, we need to have base 2 and exponent 3

Here, we can evaluate like  2³

Here 2³= 8

Inversely if we  give the base 2 and it produces 8 like

2³ = 8 then what is the exponent that will produce 8?

That exponent is called algorithm.  We call the exponent 3 the logarithm of 8 with base 2.  

We write it like, 3 = log₂8

The base 2 is written as a subscript.

3 is the exponent to which 2 must be raised to produce 8

A logarithm is an exponent.

if 10⁴ = 10,000 then,

log₁₀ 10,000 = 4

The logarithm of 10,000 with base 10 is 4

4 is the exponent to which 10 must be raised to produce 10,000

10⁴ = 10,000 is called the exponential form.

log₁₀ 10,000 = 4 is called the logarithmic form.

Here is the definition log_b x = n means bⁿ = x