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If log10(5) = a, what is log10(25) in terms of a?

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Question: If log10(5) = a, what is log10(25) in terms of a?

Options:

  1. 2a
  2. a
  3. a/2
  4. 4a

Correct Answer: 2a

Solution: 

log10(25) = log10(5^2) = 2 * log10(5) = 2a.

If log10(5) = a, what is log10(25) in terms of a?

Practice Questions

Q1
If log10(5) = a, what is log10(25) in terms of a?
  1. 2a
  2. a
  3. a/2
  4. 4a

Questions & Step-by-Step Solutions

If log10(5) = a, what is log10(25) in terms of a?
Correct Answer: 2a
  • Step 1: Understand that log10(5) is given as 'a'.
  • Step 2: Recognize that 25 can be written as 5 squared (5^2).
  • Step 3: Use the logarithm property that states log10(x^y) = y * log10(x).
  • Step 4: Apply this property to log10(25): log10(25) = log10(5^2).
  • Step 5: Rewrite log10(25) using the property: log10(25) = 2 * log10(5).
  • Step 6: Substitute log10(5) with 'a': log10(25) = 2 * a.
  • Logarithmic Properties – Understanding the properties of logarithms, particularly the power rule which states that log_b(x^n) = n * log_b(x).
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