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

Formula

The limit of (ln (1 + x))/x as x → 0 is
1.

Limit of (loga (1 + x))/x

Example

Example

Solution

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.