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

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.