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If logb(64) = 6, what is the value of b?

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Question: If logb(64) = 6, what is the value of b?

Options:

  1. 2
  2. 4
  3. 8
  4. 16

Correct Answer: 8

Solution: 

64 = b^6, so b = 64^(1/6) = 2.

If logb(64) = 6, what is the value of b?

Practice Questions

Q1
If logb(64) = 6, what is the value of b?
  1. 2
  2. 4
  3. 8
  4. 16

Questions & Step-by-Step Solutions

If logb(64) = 6, what is the value of b?
Correct Answer: 2
  • Step 1: Understand that logb(64) = 6 means that b raised to the power of 6 equals 64.
  • Step 2: Write the equation from the logarithm: b^6 = 64.
  • Step 3: To find b, we need to take the sixth root of 64. This can be written as b = 64^(1/6).
  • Step 4: Calculate the sixth root of 64. Since 2^6 = 64, we find that b = 2.
  • Logarithms – Understanding the relationship between logarithms and exponents, specifically how to convert from logarithmic form to exponential form.
  • Exponents – Applying the properties of exponents to simplify expressions and solve for the base.
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