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If log_10(2) = 0.301, what is log_10(20)? (2023)

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Question: If log_10(2) = 0.301, what is log_10(20)? (2023)

Options:

  1. 0.301
  2. 0.699
  3. 1.301
  4. 1.699

Correct Answer: 1.301

Exam Year: 2023

Solution:

log_10(20) = log_10(2) + log_10(10) = 0.301 + 1 = 1.301.

If log_10(2) = 0.301, what is log_10(20)? (2023)

Practice Questions

Q1
If log_10(2) = 0.301, what is log_10(20)? (2023)
  1. 0.301
  2. 0.699
  3. 1.301
  4. 1.699

Questions & Step-by-Step Solutions

If log_10(2) = 0.301, what is log_10(20)? (2023)
  • Step 1: Understand that log_10(20) can be broken down using the property of logarithms that states log_b(m * n) = log_b(m) + log_b(n).
  • Step 2: Rewrite 20 as 2 * 10, so we have log_10(20) = log_10(2 * 10).
  • Step 3: Apply the property from Step 1: log_10(20) = log_10(2) + log_10(10).
  • Step 4: Substitute the known values: log_10(2) = 0.301 and log_10(10) = 1 (since log base 10 of 10 is 1).
  • Step 5: Calculate the sum: log_10(20) = 0.301 + 1.
  • Step 6: Final result: log_10(20) = 1.301.
  • Logarithmic Properties – The question tests the understanding of the properties of logarithms, specifically the product rule which states that log_b(mn) = log_b(m) + log_b(n).
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