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

Practice Questions

Q1
Which of the following is true for log_a(b) and log_a(c) if b < c? (2019)
  1. log_a(b) < log_a(c)
  2. log_a(b) > log_a(c)
  3. log_a(b) = log_a(c)
  4. None of the above

Questions & Step-by-Step Solutions

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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