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If log_x(64) = 6, what is the value of x? (2023)

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Question: If log_x(64) = 6, what is the value of x? (2023)

Options:

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

Correct Answer: 8

Exam Year: 2023

Solution: 

log_x(64) = 6 implies x^6 = 64. Since 64 = 2^6, we have x = 2.

If log_x(64) = 6, what is the value of x? (2023)

Practice Questions

Q1
If log_x(64) = 6, what is the value of x? (2023)
  1. 2
  2. 4
  3. 8
  4. 16

Questions & Step-by-Step Solutions

If log_x(64) = 6, what is the value of x? (2023)
  • Step 1: Understand the equation log_x(64) = 6. This means that x raised to the power of 6 equals 64.
  • Step 2: Rewrite the equation in exponential form: x^6 = 64.
  • Step 3: Recognize that 64 can be expressed as a power of 2: 64 = 2^6.
  • Step 4: Now we have the equation x^6 = 2^6.
  • Step 5: Since the bases are the same (both are raised to the power of 6), we can set the bases equal to each other: x = 2.
  • Logarithmic Equations – Understanding how to manipulate logarithmic equations to find the base.
  • Exponential Equations – Converting logarithmic forms to exponential forms to solve for unknowns.
  • Properties of Exponents – Recognizing powers of numbers, such as 64 being 2 raised to the 6th power.
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