Exercise 52 Page 304

Recall that, according to the Property of Equality for Exponential Equations , if two powers with the same base — different from 1 — are equal, then the exponents must be equal. This allows us to solve exponential equations by reducing them to a simpler equivalent equation. 4^(x+1) = 4^2 ⇔ x+1 = 2We can write an exponential equation with two solutions by working backwards. For example, we can think of an equation having two solutions first. An example is shown below. x^2=4 This equation has two solutions, x=2 and x=- 2. Now we can write an exponential equation that reduces to the equation above by using the left- and right-hand sides as exponents of a common base. This is illustrated below. 4^(x^2)=4^4 Now we have an exponential equation which has two solutions, x=2 and x=- 2.