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The solution to the equation \(\log_x 1000 - \log_x x^2 + (10^{-3})^0 = 0\) is \(x = 1000\).

Would you like any further explanation? Here are 5 related questions to expand your understanding:

1. How do logarithmic properties help simplify equations?
2. Why is \((10^{-3})^0 = 1\)?
3. What is the inverse operation of a logarithm?
4. Can logarithms have bases other than 10 and \(e\)?
5. How would the equation change if the base of the logarithm was different?

**Tip:** When solving logarithmic equations, use properties like the power rule and quotient rule to simplify the terms efficiently.

Solve the logarithmic equation log_x 1000 - log_x x^2 + (10^{-3})^0 = 0. Learn key logarithmic properties and theorems for simplifying expressions. Suitable for high school students in Grades 10-12.

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