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!