Question

Consider the function.

f(x)=2log5(x−2)+1

On what interval is the function positive?

Enter your answer in the box. Round to the nearest hundredth.

Answer 1

The function is positive when its output, f(x), is greater than zero.

2log5(x−2)+1 > 0

2log5(x−2) > -1

log5(x−2) > -1/2

x - 2 > 5^(-1/2)

x - 2 > 0.4472

x > 2.4472

Therefore, the function is positive when x is greater than 2.4472.

The interval on which the function is positive is (2.45, infinity).