ln(400/x)=20

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Solution for ln(400/x)=20 equation:


D( x )

x = 0

400/x <= 0

x = 0

x = 0

400/x <= 0

400/x <= 0

400*x^-1 <= 0

400*x^-1 <= 0 // : 400

x^-1 <= 0/400

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)

x in (0:+oo)

ln(400/x) = 20 // - 20

ln(400/x)-20 = 0

ln(400/x)-20 = 0 // + 20

ln(400/x) = 20

ln(400/x) = ln(e^20)

400/x = e^20

400/x-e^20 = 0

400*x^-1 = e^20 // : 400

x^-1 = (e^20)/400

-1 < 0

1/(x^1) = (e^20)/400 // * x^1

1 = ((e^20)/400)*x^1 // : (e^20)/400

400*e^-20 = x^1

x = 0

x in { 0}

x belongs to the empty set

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