Solution 3.3:3g
From Förberedande kurs i matematik 1
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- | {{ | + | Using the logarithm law, <math>\lg a-\lg b = \lg\frac{a}{b}\,</math>, the expression can be calculated as |
- | < | + | |
- | {{ | + | {{Displayed math||<math>\log_3 12 - \log_3 4 = \log_3\frac{12}{4} = \log _3 3 = 1\,\textrm{.}</math>}} |
+ | |||
+ | Another way is to write <math>12 = 3\cdot 4</math> and use the logarithm law, | ||
+ | <math>\lg (ab) = \lg a + \lg b\,</math>, | ||
+ | |||
+ | {{Displayed math||<math>\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}</math>}} |
Current revision
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} |