# Exponential Inequalities

How to solve exponential inequalities problems: examples and their solutions.

## Example 1

Make both side's bases the same.

2^{5x - 9} > 2^{2x}

Compare the exponents.

The bases of both sides (2) are greater than 1.

Then the order of the inequality sign doesn't change.

So 5*x* - 9 > 2*x*.

## Example 2

Make both side's bases the same.

2^{-2 - 3x} ≤ 2^{-4x}

Compare the exponents.

The bases both sides (2) are greater than 1.

Then the order of the inequality sign doesn't change.

So -2 - 3*x* ≤ -4*x*.

## Example 2: Another Solution

Let's solve the same example

by making the base to 1/2.

(1/2)^{2 + 3x} ≤ (1/2)^{4x}

Compare the exponents.

The bases both sides (1/2) are in between 0 and 1.

Then the order of the inequality sign changes.

So 2 + 3*x* ≥ 4*x*.