Question

Select the correct answer from each drop-down menu. For all positive values of x, the value of logₓ is always __________ and the value of logₓ 1 is always __________.

Answer 1

For all positive values of x, the value of logₓ is always positive and the value of logₓ 1 is always 0.

Step-by-step explanation:

For all positive values of x, the value of logₓ is always positive and the value of logₓ 1 is always 0.

The logarithm of a number represents the power to which the base must be raised to equal that number. When x is positive, the logarithm of x is always positive because the base is raised to a positive power to equal x. For example, log₂ 8 = 3, because 2³ = 8.

The logarithm of 1 is always 0, regardless of the base. This is because any number raised to the power of 0 equals 1. For example, log₉ 1 = 0, because 9⁰ = 1.