ln(3x^2-1)/ln(2x+4)

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Solution for ln(3x^2-1)/ln(2x+4) equation:


D( x )

2*x+4 <= 0

3*x^2-1 <= 0

ln(2*x+4) = 0

2*x+4 <= 0

2*x+4 <= 0

2*x+4 <= 0 // - 4

2*x <= -4 // : 2

x <= -4/2

x <= -2

3*x^2-1 <= 0

3*x^2-1 <= 0

3*x^2 <= 1

3*x^2 <= 1 // : 3

x^2 <= 1/3

x^2 <= 1/3 // ^ 1/2

abs(x) <= (1/3)^(1/2)

x in <-(1/3)^(1/2):(1/3)^(1/2)>

ln(2*x+4) = 0

ln(2*x+4) = 0

ln(2*x+4) = ln(e^0)

2*x+4 = e^0

2*x-e^0+4 = 0

2*x+3 = 0 // - 3

2*x = -3 // : 2

x = -3/2

x in (-2:-3/2) U (-3/2:-(1/3)^(1/2)) U ((1/3)^(1/2):+oo)

ln(3*x^2-1)/ln(2*x+4) = 0

ln(3*x^2-1)/ln(2*x+4) = 0 // * ln(2*x+4)

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

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

3*x^2-1 = e^0

3*x^2-e^0-1 = 0

3*x^2 = 2 // : 3

x^2 = 2/3

x^2 = 2/3 // ^ 1/2

abs(x) = (2/3)^(1/2)

x = (2/3)^(1/2) or x = -(2/3)^(1/2)

x in { (2/3)^(1/2), -(2/3)^(1/2) }

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