# what is the relationship of log, ln, e^x...etc

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### 1 Answer

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