The logarithmic equation you've provided is:

\[
\log_x(64) = 6
\]

This means that the base \( x \), raised to the power of 6, must equal 64. Mathematically, we can express this as:

\[
x^6 = 64
\]

To find \( x \), we take the sixth root of both sides:

\[
x = \sqrt[6]{64}
\]

Since \( 64 = 2^6 \), we can rewrite this as:

\[
x = 2
\]

Thus, the solution to the equation is:

\[
x = 2
\]

Would you like more details on how logarithms work or on the steps involved?

Here are 5 related questions for you to explore:
1. What is the general form of a logarithmic equation?
2. How can you change the base of a logarithmic function?
3. What are the properties of logarithms, such as the product or quotient rules?
4. How can you solve equations involving logarithms with different bases?
5. How does the change-of-base formula for logarithms work?

**Tip:** Always remember that \(\log_b(a) = c\) is equivalent to \(b^c = a\). This is a fundamental relationship between exponentials and logarithms.

Learn how to solve the logarithmic equation log_x(64) = 6, which involves finding the base x such that x raised to the power of 6 equals 64. This step-by-step guide covers key logarithmic and exponential concepts, including the relationship between logarithms and exponents. Suitable for high school students in Grades 9-12.

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