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If log_5(x) = 1/2, what is the value of x?

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Question: If log_5(x) = 1/2, what is the value of x?

Options:

  1. 5
  2. 25
  3. sqrt(5)
  4. 1/5

Correct Answer: sqrt(5)

Solution: 

log_5(x) = 1/2 implies x = 5^(1/2) = sqrt(5).

If log_5(x) = 1/2, what is the value of x?

Practice Questions

Q1
If log_5(x) = 1/2, what is the value of x?
  1. 5
  2. 25
  3. sqrt(5)
  4. 1/5

Questions & Step-by-Step Solutions

If log_5(x) = 1/2, what is the value of x?
  • Step 1: Understand that log_5(x) = 1/2 means that x is the number you get when you raise 5 to the power of 1/2.
  • Step 2: Rewrite the equation in exponential form: x = 5^(1/2).
  • Step 3: Recognize that 5^(1/2) is the same as the square root of 5.
  • Step 4: Therefore, x = sqrt(5).
  • Logarithms – Understanding the relationship between logarithms and exponents, specifically how to convert from logarithmic form to exponential form.
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