Aus Online Mathematik Brückenkurs 1

Using the logarithm law, \displaystyle \lg a-\lg b=\lg \left( \frac{a}{b} \right), the expression can be calculated as

\displaystyle \log _{3}12-\log _{3}4=\log _{3}\frac{12}{4}=\log _{3}3=1

Another way is to write \displaystyle \text{12}=\text{3}\centerdot \text{4 } and use the logarithm law, \displaystyle \lg \left( ab \right)=\lg a+\lg b,

\displaystyle \begin{align} & \log _{3}12-\log _{3}4=\log _{3}\left( 3\centerdot 4 \right)-\log _{3}4 \\ & =\log _{3}3+\log _{3}4-\log _{3}4=\log _{3}3=1 \\ \end{align}