Solution 3.3:2g
From Förberedande kurs i matematik 1
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- | {{ | + | We know that <math>10^{\lg x} = x</math>, so therefore we rewrite the exponent as |
- | < | + | <math>-\lg 0\textrm{.}1 = (-1)\cdot\lg 0\textrm{.}1 = \lg 0\textrm{.}1^{-1}</math> |
- | {{ | + | by using the log law <math>b\lg a = \lg a^b</math>. This gives |
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+ | {{Displayed math||<math>10^{-\lg 0\textrm{.}1}=10^{\lg 0\textrm{.}1^{-1}}=0\textrm{.}1^{-1}=\frac{1}{0\textrm{.}1}=10\,\textrm{.}</math>}} |
Current revision
We know that \displaystyle 10^{\lg x} = x, so therefore we rewrite the exponent as \displaystyle -\lg 0\textrm{.}1 = (-1)\cdot\lg 0\textrm{.}1 = \lg 0\textrm{.}1^{-1} by using the log law \displaystyle b\lg a = \lg a^b. This gives
\displaystyle 10^{-\lg 0\textrm{.}1}=10^{\lg 0\textrm{.}1^{-1}}=0\textrm{.}1^{-1}=\frac{1}{0\textrm{.}1}=10\,\textrm{.} |