Final answer:
To find the solution of the exponential equation 5⁻ˣ/¹⁰⁰=2, isolate x by multiplying both sides of the equation by 100, rewrite 200 as a power of 5, set the exponents equal to each other, multiply both sides by -1 to solve for x, and obtain x = -3.301 as the solution.
Step-by-step explanation:
To find the solution of the exponential equation 5-x/100 = 2, we need to isolate x. We can start by multiplying both sides of the equation by 100 to get rid of the denominator:
5-x/100 * 100 = 2 * 100
5-x = 200
Next, we can rewrite 200 as a power of 5:
5-x = 53.301
Since the bases are equal, the exponents must also be equal:
-x = 3.301
To solve for x, we can multiply both sides of the equation by -1:
x = -3.301
Therefore, the solution to the exponential equation is x = -3.301 (correct to four decimal places).