Aus Online Mathematik Brückenkurs 1

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

\displaystyle \log_3 12 - \log_3 4 = \log_3\frac{12}{4} = \log _3 3 = 1\,\textrm{.}

Another way is to write \displaystyle 12 = 3\cdot 4 and use the logarithm law, \displaystyle \lg (ab) = \lg a + \lg b\,,

\displaystyle \begin{align} \log _{3}12 - \log _{3}4 &= \log_{3}(3\cdot 4) - \log_{3} 4\\[5pt] &= \log_{3}3 + \log _{3}4 - \log _{3}4\\[5pt] &= \log _{3}3\\[5pt] &= 1\,\textrm{.} \end{align}