ln(5x^2)/ln(6x^3)

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Solution for ln(5x^2)/ln(6x^3) equation:


D( x )

6*x^3 <= 0

ln(6*x^3) = 0

5*x^2 <= 0

6*x^3 <= 0

6*x^3 <= 0

6*x^3 <= 0

6*x^3 <= 0 // : 6

x^3 <= 0/6

x^3 <= 0

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

x <= 0

x in (-oo:0>

ln(6*x^3) = 0

ln(6*x^3) = 0

ln(6*x^3) = ln(e^0)

6*x^3 = e^0

6*x^3-e^0 = 0

6*x^3 = 1 // : 6

x^3 = 1/6

x^3 = 1/6 // ^ 1/3

x = (1/6)^(1/3)

5*x^2 <= 0

5*x^2 <= 0

5*x^2 <= 0

5*x^2 <= 0 // : 5

x^2 <= 0/5

x^2 <= 0

x in <0:0>

x in (0:(1/6)^(1/3)) U ((1/6)^(1/3):+oo)

ln(5*x^2)/ln(6*x^3) = 0

ln(5*x^2)/ln(6*x^3) = 0 // * ln(6*x^3)

ln(5*x^2) = 0

ln(5*x^2) = ln(e^0)

5*x^2 = e^0

5*x^2-e^0 = 0

5*x^2 = 1 // : 5

x^2 = 1/5

x^2 = 1/5 // ^ 1/2

abs(x) = (1/5)^(1/2)

x = (1/5)^(1/2) or x = -(1/5)^(1/2)

x in { -(1/5)^(1/2)}

x = (1/5)^(1/2)

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