Lösung 3.3:2a

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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

Vorlage:Displayed math

should hold. In this case, we see that

Vorlage:Displayed math

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