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Which of the following expressions is equivalent to log_5(25) + log_5(5)?

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Question: Which of the following expressions is equivalent to log_5(25) + log_5(5)?

Options:

  1. log_5(125)
  2. log_5(30)
  3. log_5(20)
  4. log_5(10)

Correct Answer: log_5(125)

Solution: 

Using the property of logarithms, log_5(25) = 2 and log_5(5) = 1. Therefore, log_5(25) + log_5(5) = 2 + 1 = 3, which is log_5(125).

Which of the following expressions is equivalent to log_5(25) + log_5(5)?

Practice Questions

Q1
Which of the following expressions is equivalent to log_5(25) + log_5(5)?
  1. log_5(125)
  2. log_5(30)
  3. log_5(20)
  4. log_5(10)

Questions & Step-by-Step Solutions

Which of the following expressions is equivalent to log_5(25) + log_5(5)?
  • Step 1: Identify the logarithmic expressions: log_5(25) and log_5(5).
  • Step 2: Simplify log_5(25). Since 25 is 5 squared (5^2), log_5(25) equals 2.
  • Step 3: Simplify log_5(5). Since 5 is 5 to the power of 1 (5^1), log_5(5) equals 1.
  • Step 4: Add the results from Step 2 and Step 3: 2 + 1 equals 3.
  • Step 5: Recognize that 3 can be expressed as log_5(125) because 125 is 5 cubed (5^3).
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