Algebra-2

To compare and , we need to analyze the behavior of the logarithmic function and the expression inside the logarithm.

Simplify the expression inside the logarithm

The expression inside the logarithm is a quadratic:

This shows that the quadratic is always greater than or equal to 2, because the term is always non-negative, and the minimum value occurs when , where . Therefore, the minimum value of is 2, which occurs at .

Thus, for all , the value of is always greater than or equal to 2.

Compare the logarithmic expressions

The logarithmic function is an increasing function because the base is greater than 1. This means that if

Click "Show Answer" to reveal the answer and analysis