Question

Find the exact solution to the equation. (5 points)

one hundred times one fifth to the power of quantity x divided by four equals four.

Answer 1

x = 2

Explanation:

We can start by rewriting the equation as follows:

100 * (1/5)^x / 4 = 4

Next, we'll multiply both sides by 4 to cancel out the division by 4:

400 * (1/5)^x = 16

Finally, we'll divide both sides by 400 * (1/5)^x to isolate (1/5)^x:

1/((1/5)^x) = 16 / 400 = 1/25

Taking the reciprocal of both sides:

(1/5)^x = 25

Taking the power of 5 to both sides:

x = log(25)/log(5) = 2

So x = 2 is the solution to the equation.