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

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

Options:

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

Correct Answer: 8

Solution: 

x = 64^(1/6) = 2.

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

Practice Questions

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

Questions & Step-by-Step Solutions

If logx(64) = 6, what is the value of x?
Correct Answer: 2
  • Step 1: Understand the equation logx(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: To find x, we need to take the sixth root of 64. This can be written as x = 64^(1/6).
  • Step 4: Calculate 64^(1/6). Since 64 is 2 raised to the power of 6 (because 2^6 = 64), we can simplify it: 64^(1/6) = (2^6)^(1/6).
  • Step 5: When you raise a power to a power, you multiply the exponents: (2^6)^(1/6) = 2^(6 * (1/6)) = 2^1.
  • Step 6: Therefore, x = 2.
  • Logarithmic Equations – Understanding how to manipulate logarithmic equations to solve for the base.
  • Exponential Functions – Using properties of exponents to rewrite logarithmic expressions.
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