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100-x-lg-x-x-3-Find-x-




Question Number 207207 by hardmath last updated on 09/May/24
100 x^(lg x)   =  x^3   Find:  x = ?
$$\mathrm{100}\:\mathrm{x}^{\boldsymbol{\mathrm{lg}}\:\boldsymbol{\mathrm{x}}} \:\:=\:\:\mathrm{x}^{\mathrm{3}} \\ $$$$\mathrm{Find}:\:\:\mathrm{x}\:=\:? \\ $$
Answered by mr W last updated on 09/May/24
100=x^(3−log x)   100=10^2 =10^(3−1) =10^(3−log 10)   ⇒x=10
$$\mathrm{100}={x}^{\mathrm{3}−\mathrm{log}\:{x}} \\ $$$$\mathrm{100}=\mathrm{10}^{\mathrm{2}} =\mathrm{10}^{\mathrm{3}−\mathrm{1}} =\mathrm{10}^{\mathrm{3}−\mathrm{log}\:\mathrm{10}} \\ $$$$\Rightarrow{x}=\mathrm{10} \\ $$

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