MatemáticasBásico1 respuestas

Encontrar el valor de x?

Encontrar el valor de x? Log(x - 9) + log100x = 3.

En resumen

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Mejor respuesta

Jacky2000
10

<img src="https://tex.z-dn.net/?f=%5Clog%28x-9%29%2B%5Clog100x%3D3%5C%5C%0AD%3Ax-9%3E0%20%5Cwedge%20100x%3E0%5C%5C%0AD%3Ax%3E9%20%5Cwedge%20x%3E0%5C%5C%0AD%3Ax%3E9%5C%5C%0A%5Clog100x%28x-9%29%3D3%5C%5C%0A10%5E3%3D100x%28x-9%29%5C%5C%0A10%3Dx%28x-9%29%5C%5C%0Ax%5E2-9x-10%3D0%5C%5C%0Ax%5E2%2Bx-10x-10%3D0%5C%5C%0Ax%28x%2B1%29-10%28x%2B1%29%3D0%5C%5C%0A%28x-10%29%28x%2B1%29%3D0%5C%5C%0Ax%3D10%20%5Cvee%20x%3D-1%5C%5C%0A-1%5Cnot%20%5Cin%20D%20%5CRightarrow%20x%3D10%0A%0A" />0 \ wedge 100x>0 \ \ &#10 ; D : x>9 \ wedge x>0 \ \ &#10 ; D : x>9 \ \ &#10 ; \ log100x(x - 9) = 3 \ \ &#10 ; 10 ^ 3 = 100x(x - 9) \ \ &#10 ; 10 = x(x - 9) \ \ &#10 ; x ^ 2 - 9x - 10 = 0 \ \ &#10 ; x ^ 2 + x - 10x - 10 = 0 \ \ &#10 ; x(x + 1) - 10(x + 1) = 0 \ \ &#10 ; (x - 10)(x + 1) = 0 \ \ &#10 ; x = 10 \ vee x = - 1 \ \ &#10 ; - 1 \ not \ in D \ Rightarrow x = 10&#10 ; &#10 ; " alt = " \ log(x - 9) + \ log100x = 3 \ \ &#10 ; D : x - 9>0 \ wedge 100x>0 \ \ &#10 ; D : x>9 \ wedge x>0 \ \ &#10 ; D : x>9 \ \ &#10 ; \ log100x(x - 9) = 3 \ \ &#10 ; 10 ^ 3 = 100x(x - 9) \ \ &#10 ; 10 = x(x - 9) \ \ &#10 ; x ^ 2 - 9x - 10 = 0 \ \ &#10 ; x ^ 2 + x - 10x - 10 = 0 \ \ &#10 ; x(x + 1) - 10(x + 1) = 0 \ \ &#10 ; (x - 10)(x + 1) = 0 \ \ &#10 ; x = 10 \ vee x = - 1 \ \ &#10 ; - 1 \ not \ in D \ Rightarrow x = 10&#10 ; &#10 ; " align = "absmiddle" class = "latex - formula">.