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Exponential Equations

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Presentation on theme: "Exponential Equations"— Presentation transcript:

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


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