SUMMARY
The domain of the function $$log_{10}(x²)$$ is confirmed to be the same as that of $$2log_{10}(|x|)$$, which is defined for all non-zero real numbers. The x-intercepts for both forms are found to be x = {-1, 1} for $$log_{10}(x²)$$ and x = {1} for $$2log_{10}(x)$$. However, the correct interpretation of the simplified form is $$2log_{10}(|x|)$$, which retains the x-intercepts of the original function.
PREREQUISITES
- Understanding of logarithmic functions, specifically base 10 logarithms.
- Knowledge of absolute values in mathematical expressions.
- Familiarity with solving equations for x-intercepts.
- Basic algebraic manipulation skills, including simplification of logarithmic expressions.
NEXT STEPS
- Study the properties of logarithmic functions, focusing on transformations and simplifications.
- Learn about the implications of absolute values in logarithmic equations.
- Explore the concept of x-intercepts in various types of functions.
- Practice solving logarithmic equations with different bases and forms.
USEFUL FOR
Students studying algebra, particularly those focusing on logarithmic functions, as well as educators seeking to clarify common misconceptions about logarithmic identities and their domains.