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If log_a(64) = 6, what is the value of a?

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Question: If log_a(64) = 6, what is the value of a?

Options:

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

Correct Answer: 8

Solution: 

log_a(64) = 6 implies a^6 = 64. Since 64 = 2^6, we have a = 2.

If log_a(64) = 6, what is the value of a?

Practice Questions

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

Questions & Step-by-Step Solutions

If log_a(64) = 6, what is the value of a?
  • Step 1: Understand the equation log_a(64) = 6. This means that 'a' raised to the power of 6 equals 64.
  • Step 2: Rewrite the equation in exponential form: a^6 = 64.
  • Step 3: Recognize that 64 can be expressed as a power of 2. Specifically, 64 = 2^6.
  • Step 4: Now we have a^6 = 2^6. This means that 'a' must be equal to 2 because both sides have the same exponent (6).
  • Step 5: Therefore, the value of 'a' is 2.
  • Logarithmic Equations – Understanding how to manipulate logarithmic equations to find the base.
  • Exponential Form – Converting logarithmic expressions into exponential form to solve for unknowns.
  • Properties of Exponents – Recognizing and applying properties of exponents, such as identifying powers of numbers.
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