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If log_5(25) = x, what is the value of x?

Practice Questions

Q1
If log_5(25) = x, what is the value of x?
  1. 1
  2. 2
  3. 3
  4. 4

Questions & Step-by-Step Solutions

If log_5(25) = x, what is the value of x?
Correct Answer: 2
  • Step 1: Understand that log_5(25) means 'to what power must 5 be raised to get 25?'
  • Step 2: Recognize that 25 can be written as 5 raised to the power of 2, which is 5^2.
  • Step 3: Rewrite the equation: log_5(25) = log_5(5^2).
  • Step 4: Use the property of logarithms that says log_b(a^c) = c * log_b(a).
  • Step 5: Apply this property: log_5(5^2) = 2 * log_5(5).
  • Step 6: Know that log_5(5) equals 1 because 5 raised to the power of 1 is 5.
  • Step 7: Substitute back: 2 * log_5(5) = 2 * 1 = 2.
  • Step 8: Conclude that x = 2.
  • Logarithmic Properties – Understanding how to simplify logarithms using the property that log_b(a^c) = c * log_b(a).
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