# How do you find the limit of #ln(2x)-ln(1+x)# as x approaches infinity?

##### 1 Answer

Jan 26, 2017

Use the property that the difference to two logarithms is division within argument.

Use L'Hôpital's rule on argument.

#### Explanation:

Given:

Use the property that the difference to two logarithms is division within argument.

Use L'Hôpital's rule

Compute the derivative of the numerator:

Compute the derivative of the denominator:

The new expression is:

Therefore, the original limit is the same: