Which of the following is true for log_a(b) and log_a(c) if b < c? (2019)

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Question: Which of the following is true for log_a(b) and log_a(c) if b < c? (2019)

Options:

Correct Answer: log_a(b) < log_a(c)

Exam Year: 2019

Solution:

If a > 1, then log_a(b) < log_a(c) when b < c.

Which of the following is true for log_a(b) and log_a(c) if b < c? (2019)

Which of the following is true for log_a(b) and log_a(c) if b < c? (2019)

Step 1: Understand what log_a(b) means. It is the power you need to raise 'a' to get 'b'.
Step 2: Recognize that if b < c, then b is smaller than c.
Step 3: If a > 1, the logarithm function is increasing. This means as the input (b or c) increases, the output (log_a(b) or log_a(c)) also increases.
Step 4: Since b < c, and the logarithm function is increasing, it follows that log_a(b) < log_a(c).
Step 5: Therefore, if a > 1 and b < c, then log_a(b) is less than log_a(c).

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