ln(3x^-4)/(x-7)^6

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Solution for ln(3x^-4)/(x-7)^6 equation: 


D( x )

(x-7)^6 = 0

x = 0

3*x^-4 <= 0

(x-7)^6 = 0

(x-7)^6 = 0

x-7 = 0 // + 7

x = 7

x = 0

x = 0

3*x^-4 <= 0

3*x^-4 <= 0

3*x^-4 <= 0

3*x^-4 <= 0 // : 3

x^-4 <= 0/3

x^-4 <= 0

1/(x^4) <= 0

x <> 0

1/(x^4) <= 0 // * x^8

(x^8)/(x^4) <= 0

x^4 <= 0

x belongs to the empty set

x in (-oo:0) U (0:7) U (7:+oo)

ln(3*x^-4)/((x-7)^6) = 0

ln(3*x^-4)/((x-7)^6) = 0 // * (x-7)^6

ln(3*x^-4) = 0

ln(3*x^-4) = ln(e^0)

3*x^-4 = e^0

3*x^-4-e^0 = 0

3*x^-4 = 1 // : 3

x^-4 = 1/3

-4 < 0

1/(x^4) = 1/3 // * x^4

1 = 1/3*x^4 // : 1/3

3 = x^4

x^4 = 3 // ^ 1/4

abs(x) = 3^(1/4)

x = 3^(1/4) or x = -3^(1/4)

x in { 3^(1/4), -3^(1/4) }

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