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If log_b(25) = 2, what is the value of b?

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Question: If log_b(25) = 2, what is the value of b?

Options:

  1. 5
  2. 10
  3. 25
  4. 50

Correct Answer: 5

Solution: 

log_b(25) = 2 implies b^2 = 25. Therefore, b = 5.

If log_b(25) = 2, what is the value of b?

Practice Questions

Q1
If log_b(25) = 2, what is the value of b?
  1. 5
  2. 10
  3. 25
  4. 50

Questions & Step-by-Step Solutions

If log_b(25) = 2, what is the value of b?
  • Step 1: Understand the equation log_b(25) = 2. This means that b raised to the power of 2 equals 25.
  • Step 2: Rewrite the equation in exponential form: b^2 = 25.
  • Step 3: To find b, take the square root of both sides of the equation: b = √25.
  • Step 4: Calculate the square root of 25, which is 5.
  • Step 5: Therefore, the value of b is 5.
  • Logarithmic Equations – Understanding how to manipulate logarithmic equations to find the base.
  • Exponential Relationships – Recognizing the relationship between logarithms and exponents.
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