# Limit of (a^{x} - 1)/x

How to use the limit of Limit of (a^{x} - 1)/x to solve the given limit with an exponential function: formula, 1 example, and its solution.

## Formula

## Example

Solution

Solution (Detail)

4^{x} - 1

= 2^{2x} - 1

= (2^{x})^{2} - 1^{2}

Power of a Power

(2^{x})^{2} - 1^{2} = (2^{x} + 1)(2^{x} - 1)

Factor the Difference of Two Squares: a^{2} - b^{2}

Cancel the factors (2^{x} + 1).

The exponent of 2^{x} is x.

The denominator is also x.

So, as x → 0,

(2^{x} - 1)/x → ln 2.

So ln 2 is the answer.