eldos1306 eldos1306
  • 03-09-2016
  • Mathematics
contestada

x^lg(x)=100^x find x

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Аноним Аноним
  • 03-09-2016

[tex]x^lg(x)=100^x[/tex]


[tex]X^lg(x)=100^x:x[/tex]  [tex]|Solve \ for \ x|[/tex]


[tex]|Use \ logarithms \ of \ both \ sides \ of \ the \ base \ 10| [/tex]


[tex]lg (x ^ lg (x)) = lg (100x) [/tex]


[tex]lg ^ 2 (x) = 2 + lgx[/tex]


[tex]lg 2 ^ x-lg x -2 = 0[/tex]


[tex]lg x = 2 x = 100[/tex]


[tex]lg x = -1 x = \dfrac{1}{10} = 0.1[/tex]

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