2-ln(3x)=ln(x/12)

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Solution for 2-ln(3x)=ln(x/12) equation:


D( x )

x/12 <= 0

3*x <= 0

x/12 <= 0

x/12 <= 0

1/12*x+0 <= 0 // - 0

1/12*x <= 0 // : 1/12

x <= 0/1/12

x <= 0

3*x <= 0

3*x <= 0

3*x+0 <= 0 // - 0

3*x <= 0 // : 3

x <= 0/3

x <= 0

x in (0:+oo)

2-ln(3*x) = ln(x/12) // - ln(x/12)

2-ln(3*x)-ln(x/12) = 0

ln(1/(3*x))-ln(x/12)+2 = 0

ln((1/(3*x))/(x/12))+2 = 0

ln((1/(3*x))/(x/12))+ln(1*e^2) = 0

ln((1/(3*x))/(x/12))+2 = 0 // - 2

ln((1/(3*x))/(x/12)) = -2

ln((1/(3*x))/(x/12)) = ln(e^-2)

(1/(3*x))/(x/12) = e^-2

(1/(3*x))/(x/12)-e^-2 = 0

4*x^-2 = e^-2 // : 4

x^-2 = (e^-2)/4

-2 < 0

1/(x^2) = (e^-2)/4 // * x^2

1 = ((e^-2)/4)*x^2 // : (e^-2)/4

4*e^2 = x^2

x^2 = 4*e^2 // ^ 1/2

abs(x) = 2*e

x = 2*e or x = -(2*e)

x in { -(2*e)}

x = 2*e

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