ln(1/x)+ln(2x^3)=ln(8)

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Solution for ln(1/x)+ln(2x^3)=ln(8) equation: 


D( x )

x = 0

1/x <= 0

2*x^3 <= 0

x = 0

x = 0

1/x <= 0

1/x <= 0

1*x^-1 <= 0

1*x^-1 <= 0 // : 1

x^-1 <= 0/1

x^-1 <= 0

1/(x^1) <= 0

x <> 0

1/(x^1) <= 0 // * x^2

(x^2)/(x^1) <= 0

x^1 <= 0

x <= 0

x in (-oo:0)

2*x^3 <= 0

2*x^3 <= 0

2*x^3 <= 0

2*x^3 <= 0 // : 2

x^3 <= 0/2

x^3 <= 0

x^3 <= 0 // ^ 1/3

x <= 0

x in (-oo:0>

x in (0:+oo)

ln(1/x)+ln(2*x^3) = ln(8) // - ln(8)

ln(1/x)+ln(2*x^3)-ln(8) = 0

ln(1*(1/x))+ln(2*x^3)-ln(8) = 0

ln(1*2*(1/x)*x^3)-ln(8) = 0

ln(1*2*(1/x)*x^3)+ln(1/8) = 0

ln(1*2*(1/x)*x^3)+ln(1/8) = 0 // - ln(1/8)

ln(1*2*(1/x)*x^3) = -ln(1/8)

1*2*(1/x)*x^3 = 1/1/8

1*2*(1/x)*x^3-(1/1/8) = 0

2*x^2 = 8 // : 2

x^2 = 4

x^2 = 4 // ^ 1/2

abs(x) = 2

x = 2 or x = -2

x in { -2} 

x = 2

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