# Limit of (ln (1 + x))/x

How to use the limit of Limit of (ln (1 + x))/x to solve the given limit with a logarithmic function: formula, 1 example, and its solution.

## Formula

## Examplelim_{x → 0} [ln (1 + 2x)]/x

Solution

Solution (Detail)

First write the limit part and [ln (1 + 2x)].

The inner part of [ln (1 + 2x)] is (1 + 2x).

So write 2x

in the denominator.

The denominator of the given expression is x.

But you wrote 2x.

So, to undo the denominator 2,

multiply 2.

So (ln (1 + 2x))/x = [(ln (1 + 2x))/2x]⋅2.

As x → 0,

(ln (1 + 2x))/2x → 1

and write the constant 2.

1⋅2 = 2

So 2 is the answer.