Question

For the logarithmic function g(x) = log x (base a), where a>1, is the function increasing or decreasing over its entire domain?Choose the correct answer below.O A. Decreasing, because a logarithmic function always decreases.O B. Increasing, because a logarithmic function always increases.O C. Decreasing, because a > 1.O D. Increasing, because a > 1.

Answer 1

D. Increasing, because a > 1.

Explanation:

Given the logarithmic function:

`\log_ax,a>1`

We want to determine if the function is increasing or decreasing.

For any logarithm function:

• If the base, a > 1, the function is increasing over its entire domain.

,

• If the base, 0Thus, in our case, the function is increasing, because a > 1.

Option D is correct.