Math Problem Statement

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

Solution

Let's break down and solve the equation:

log⁡x(1000)−log⁡(x2)+(10−3)0=0\log_x(1000) - \log(x^2) + (10^{-3})^0 = 0

Step 1: Simplify the terms

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

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

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Math Problem Analysis

Mathematical Concepts

Logarithms
Exponents
Properties of Logarithms

Formulas

Change of Base Formula: log_a(b) = log_c(b) / log_c(a)
Logarithm of a Power: log_a(x^n) = n * log_a(x)
Property: (a^0) = 1

Theorems

Properties of Logarithms
Exponential Rules

Suitable Grade Level

Grades 10-12

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