Solution 3.3:2c

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Current revision (14:30, 1 October 2008) (edit) (undo)
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Because
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Because <math>\mathop{\text{lg}} 0\textrm{.}001</math> is defined as the exponent that should stand in the coloured box in the equality
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<math>\text{lg }0.000\text{1}</math>
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is defined as the exponent that should stand in the grey box (??) in the equality
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{{Displayed math||<math>10^{\bbox[#FFEEAA;,1.5pt]{\phantom{\scriptstyle ??}}} = 0\textrm{.}001</math>}}
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<math>10^{??}=0.001</math>
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and we have that
and we have that
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{{Displayed math||<math>10^{-3} = 0\textrm{.}001\,,</math>}}
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<math>10^{-3}=0.001</math>
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thus <math>\mathop{\text{lg}} 0\textrm{.}0001 = -3\,</math>.
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thus
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<math>\text{lg }0.000\text{1}=-\text{3}</math>.
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Current revision

Because \displaystyle \mathop{\text{lg}} 0\textrm{.}001 is defined as the exponent that should stand in the coloured box in the equality

\displaystyle 10^{\bbox[#FFEEAA;,1.5pt]{\phantom{\scriptstyle ??}}} = 0\textrm{.}001

and we have that

\displaystyle 10^{-3} = 0\textrm{.}001\,,

thus \displaystyle \mathop{\text{lg}} 0\textrm{.}0001 = -3\,.

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