We are given the equation:

\[
\log_x(128) - \log_x(2) = 2
\]

Using the **logarithmic property**:

\[
\log_b(a) - \log_b(c) = \log_b\left(\frac{a}{c}\right)
\]

We can combine the logarithms:

\[
\log_x\left(\frac{128}{2}\right) = 2
\]

Simplifying inside the logarithm:

\[
\log_x(64) = 2
\]

Now, recall the definition of a logarithm: 

\[
\log_b(a) = c \implies b^c = a
\]

So, we rewrite this as:

\[
x^2 = 64
\]

Solving for \(x\):

\[
x = \sqrt{64} = 8
\]

Thus, the solution is:

\[
x = 8
\]

Would you like more details or have any questions?

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Here are 5 related questions to explore:
1. What are the basic properties of logarithms?
2. How do you solve equations with logarithms of different bases?
3. What happens when the base of a logarithm is a fraction?
4. How can we solve exponential equations?
5. How does the change of base formula work in logarithms?

**Tip:** Always check the domain of logarithmic functions; the base \(x\) must be positive and not equal to 1.

Discover how to solve the logarithmic equation logx(128) - logx(2) = 2 using properties of logarithms and algebra. This detailed solution is perfect for students in Grades 9-11, covering key concepts and formulas.

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