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

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

Options:

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

Correct Answer: 3

Solution: 

b^3 = 27, so b = 3.

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

Practice Questions

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

Questions & Step-by-Step Solutions

If logb(27) = 3, what is the value of b?
  • Step 1: Understand the equation logb(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 take the cube root of 27.
  • Step 4: Calculate the cube root of 27. The number that, when multiplied by itself three times, gives 27 is 3.
  • Step 5: Therefore, b = 3.
  • Logarithms – Understanding the relationship between logarithms and exponents, specifically how to convert from logarithmic form to exponential form.
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