Exponential Equations

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?

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.

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.

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.

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.

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

Let me try to solve the equation.

Follow-up question Solve .