Problem: Logarithmic function

Problem

1. Use logarithmic rule 3 (see cheat sheet) to show that $log \left( x^2 \right)=2log \left( x \right)$ .
2. Use logarithmic rule 5 (see cheat sheet) to show that $log \left( x^2 \right)=2log \left( x \right)$ .
3. Use logarithmic rule 4 (see cheat sheet) to show that $log \left( x^{-1} \right)=-log \left( x \right)$ .
4. Use logarithmic rule 5 (see cheat sheet) to show that $log \left( x^{-1} \right)=-log \left( x \right)$ .
5. Is it true that $log \left( x+y \right)=log \left( x \right)+log \left( y \right)$ ? Test with $x=1, y=1$ .
6. Is it true that $log \left( x+y \right)=log \left( x \right)⋅log \left( y \right)$ ? Test with $x=1, y=1$ .

Remember, log of a sum (or difference) cannot be simplified … in any way!