First we will start with the exponent to understand the relations.
1. a^n = b
Then we say that b is the nth power of a.
Here, we have a relation between the base a and the power n.
2. Logarithm is a relation where we write the exponent (n) as an expression of the base a and b.
==> The we write :
n = log_a b
Therefore, logarithm is a different way to write the exponent expression.
3. If we have log x for example, the base here is 10.
Therefore, every time we do not write the base (a) that means that the base is 10.
3. e^x = b
The base here is the natural number e.
Now, if we are to rewrite using logarithm we will have:
log_e b = x
But when using the natural number (e) , we use the symbol (ln) instead of log_e
==> log_e = ln