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If log_b(27) = 3, what is the value of b?

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Question: If log_b(27) = 3, what is the value of b?

Options:

  1. 3
  2. 9
  3. 27
  4. 81

Correct Answer: 3

Solution: 

log_b(27) = 3 implies b^3 = 27 => b = 3.

If log_b(27) = 3, what is the value of b?

Practice Questions

Q1
If log_b(27) = 3, what is the value of b?
  1. 3
  2. 9
  3. 27
  4. 81

Questions & Step-by-Step Solutions

If log_b(27) = 3, what is the value of b?
Correct Answer: 3
  • Step 1: Understand the equation log_b(27) = 3. This means that b raised to the power of 3 equals 27.
  • Step 2: Rewrite the equation in exponential form: b^3 = 27.
  • Step 3: To find b, we need to determine what number raised to the power of 3 gives us 27.
  • Step 4: Recognize that 3 x 3 x 3 = 27, so b = 3.
  • Logarithmic Equations – Understanding how to manipulate logarithmic equations to find the base.
  • Exponential Form – Converting logarithmic expressions into their equivalent exponential forms.
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