Solution 3.3:2a

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Current revision (14:25, 1 October 2008) (edit) (undo)
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The logarithm
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The logarithm <math>\mathop{\text{lg}} 0\textrm{.}1</math> is defined as that number which should stand in the coloured box in order that the equality
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<math>\text{lg }0.\text{1 }</math>
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is defined as that number which should stand in the (??) grey box in order that the equality
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<math>10^{??}=0.1</math>
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{{Displayed math||<math>10^{\bbox[#FFEEAA;,1.5pt]{\phantom{\scriptstyle ??}}} = 0\textrm{.}1</math>}}
should hold. In this case, we see that
should hold. In this case, we see that
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{{Displayed math||<math>10^{-1} = 0\textrm{.}1</math>}}
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<math>10^{-1}=0.1</math>
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and therefore <math>\mathop{\text{lg}} 0\textrm{.}1 = -1\,</math>.
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and therefore
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<math>\text{lg }0.\text{1}=-\text{1}</math>.
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Current revision

The logarithm \displaystyle \mathop{\text{lg}} 0\textrm{.}1 is defined as that number which should stand in the coloured box in order that the equality

\displaystyle 10^{\bbox[#FFEEAA;,1.5pt]{\phantom{\scriptstyle ??}}} = 0\textrm{.}1

should hold. In this case, we see that

\displaystyle 10^{-1} = 0\textrm{.}1

and therefore \displaystyle \mathop{\text{lg}} 0\textrm{.}1 = -1\,.

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