Question

Es para mañana Ayuda plis ​

Answer 1

2 log  - 2 log (x - 1) = 0

log (x) - log (x - 1) = 0                              Propiedad. $Log_{a}$ $x - Log_{a} y = Log_{a} \frac{x}{y}$

log($\frac{x}{x+1}$) = 0

$\frac{x}{x+1}$ = 1

x = x + 1

0 = 1          x ∉ 0

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$Log (x) = \frac{2 - Log (x)}{log (x)}$

$Log (x) . Log (x) = 2 - Log (x)$                    

$Log (x)^{2} = 2 - Log (x)$                              $Log (x) = A$

$A^{2} = 2 - A\\A^{2} + A - 2 = 0\\(A + 2)(A - 1) = 0\\A + 2 = 0 || A_{1} = -2\\A - 1 = 0 || A_{2} = 1$

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$\frac{Log (16-x^{2)} }{Log 3x-4)}=2$                                           Propiedad. $x . Log_{a}(b)= Log_{a}(b^{x} )$

$Log (16-x^{2} )=2.Log(3x-4)\\16-x^{2} =(3x-4)^{2} \\16-x^{2} = 9x^{2} -24x+16\\16-x^{2}-9x^{2} +24x-16 = 0\\ -10x^{2} +24 = 0\\-2x(5x-12)=0 (x-2)\\x(5x-12)=0\\x_{1}=0\\x_{2}=12/5$

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$Log (2) + Log (11-x^{2} )=2 Log (5-x)\\Log(2 . 11-x^{2} )=Log (5-x)^{2} \\Log (22-2x^{2} )=Log (5^{2} -2.(5).(x)+x^{2} )\\Log (22-2x^{2} )=Log (25-10x+x^{2} )\\22-2x^{2} =25-10x+x^{2} \\-3x^{2} +10x-3=0 (. -1)\\3x^{2} -10x+3=0$Trinomio de la forma ax²+ bx + c

$(3x-1). (x-3)=0\\3x-1=0\\x_{1}=1/3\\-----\\x-3=0\\x_{2} =3$