Math Problem Statement

solve for x

Solve for x: log_x 1000 - log_x x^2 + (10^{-3})^0 = 0

Solution

The solution to the equation logx1000logxx2+(103)0=0\log_x 1000 - \log_x x^2 + (10^{-3})^0 = 0 is x=1000x = 1000.

Do you want further details or have any questions?

Here are 5 related questions you might find interesting:

  1. How do we solve logarithmic equations involving different bases?
  2. What is the meaning of logx1000\log_x 1000 and how is it computed?
  3. How does the property logxx2\log_x x^2 simplify in logarithmic equations?
  4. Why does (103)0=1(10^{-3})^0 = 1 hold true, and how do exponents behave in such cases?
  5. Can we solve logarithmic equations where the base is not explicitly given?

Tip: When solving logarithmic equations, remember to consider the base of the logarithm, as it can lead to different solutions.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Exponents
Algebra

Formulas

log_a (b/c) = log_a b - log_a c
(a^m)^n = a^(m*n)
log_a a = 1

Theorems

Properties of Logarithms
Exponent Rules

Suitable Grade Level

Grades 9-12