log_x(1000) - log(x ^ 2) + (10 ^ - 3) ^ 0 = 0

Let's break down and solve the equation:

\[
\log_x(1000) - \log(x^2) + (10^{-3})^0 = 0
\]

### Step 1: Simplify the terms

1. **Term 1:** \(\log_x(1000)\)
   Using the change of base formula, we can express \(\log_x(1000)\) as:

   \[
   \log_x(1000) = \frac{\log

Learn how to solve the logarithmic equation log_x(1000) - log(x^2) + (10^-3)^0 = 0 with a detailed step-by-step solution. This problem covers important mathematical concepts such as the change of base formula, properties of logarithms, and exponential rules. Suitable for students in Grades 10-12.

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