Final answer:
In the exponential equation 5^(3-2x) = 5^-x, since the bases are the same, we can equate the exponents. Doing so and solving for x, we find that x equals 3.
Step-by-step explanation:
The question is asking to solve the exponential equation: 5(3-2x) = 5(-x). Since the bases on both sides of the equation are the same (5), you can equate the exponents: 3 - 2x = -x. This is based on the principle that if ab = ac, then b must equal c.
Now, we just need to solve this simple equation. To do that, we add 2x to both sides of the equation to get: 3 = x. So, the value of x that makes the original equation true is 3.
Learn more about Solving Exponential Equations