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

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


D( x )

4*x-3 < 0

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

4*x-3 < 0

4*x-3 < 0

4*x-3 < 0 // + 3

4*x < 3 // : 4

x < 3/4

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

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

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

4*x <= 3 // : 4

x <= 3/4

(-oo:3/4) (3/4:+oo) (4*x-3)^(1/2) NaN +

x in (3/4:+oo)

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

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

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

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

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

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

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

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

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

abs(4*x-3) = 1^2 // - 1^2

abs(4*x-3)-1^2 = 0

x in (-oo:+oo)

abs(4*x-3)

4*x-3 >= 0

4*x-3 >= 0 // + 3

4*x >= 3 // : 4

x >= 3/4

x in <3/4:+oo)

4*x-1^2-3 = 0

x in (-oo:3/4)

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

abs(4*x-3)-1^2 = 0

/ | 3-(4*x)-1^2 = 0 i x in (-oo:3/4) | 4*x-1^2-3 = 0 i x in <3/4:+oo)

x in (-oo:3/4)

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

2-4*x = 0 // - 2

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

x = -2/(-4)

x = 1/2

x in <3/4:+oo)

4*x-1^2-3 = 0

4*x-4 = 0 // + 4

4*x = 4 // : 4

x = 4/4

x = 1

x in { 1/2}

x = 1

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