1. Exponential Equations

2. Do you know how to solve these exponential equations?
An equation with an unknown index (or indices) is called an exponential equation.
For example: 27 3 = x
and are exponential equations.
Do you know how to solve these exponential equations?

3. At this step, you can apply the following property.
Take as an example. 27 3 = x 27 3 = x
Express both sides with the same base. 3 = x
At this step, you can apply the following property.

4. Express both sides with the same base.
Take as an example. 27 3 = x 27 3 = x
Express both sides with the same base. 3 = x  3 = x
For a > 0 and a ≠ 1,
if ax = ay, then x = y.

5. Do not forget to check the answer obtained.
Take as an example. 27 3 = x 27 3 = x
Express both sides with the same base. 3 = x  3 = x
Do not forget to check the answer obtained.

6. Follow-up question Solve . 4 8 = ) (2 = 2 = 3 = x ∴ 1 = x
◄ Express both sides as powers of 2. 3 2 = x 3 = x
◄ If ax = ay, then x = y. ∴ 1 = x
◄ Check whether the answer obtained satisfies the original equation.

7. How to solve some complicated exponential equations like
2x x = 6?
You can express 2x + 1 = 2(2x) first.

8. Let me try to solve the equation.

9. Follow-up question
Solve