Think about an equation with two solutions first. Can you write an exponential equation that reduces to it?
Yes, see solution.
Practice makes perfect
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 exponentsmust be equal. This allows us to solve exponential equations by reducing them to a simpler equivalent equation.
4^(x+1) = 4^2 ⇔ x+1 = 2
We 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.
