Lösung 3.3:2c

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

Vorlage:Displayed math

and we have that

Vorlage:Displayed math

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