Question

El valor de x que satisface la ecuación: log5 (x 3) log5 (x-1) = log5 5 es:.?

Answer 1

Respuesta:

$x\approx \:1.95595\dots$

Explicación paso a paso:

$\log _{10}\left(5\right)\left(x^3\right)\log _{10}\left(5\right)\left(x-1\right)=\log _{10}\left(5\right)\left(5\right)\\\\\log _{10}\left(5\right)^2x^4-\log _{10}\left(5\right)^2x^3=5\log _{10}\left(5\right)\\\\\log _{10}\left(5\right)^2x^4-\log _{10}\left(5\right)^2x^3-5\log _{10}\left(5\right)=5\log _{10}\left(5\right)-5\log _{10}\left(5\right)\\\\\log _{10}\left(5\right)^2x^4-\log _{10}\left(5\right)^2x^3-5\log _{10}\left(5\right)=0$

$0.48855\dots x^3+0.46703\dots x^2+0.91350\dots x+1.78677\dots \approx \:0\\\\0.48855\dots x^2-0.23289\dots x+1.24717\dots \approx \:0\\\\x\approx \:1.95595\dots$