log(x/4)(17x-4)=2

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Solution for log(x/4)(17x-4)=2 equation:


D( x )

x/4 <= 0

17*x-4 <= 0

x/4 <= 0

x/4 <= 0

1/4*x+0 <= 0 // - 0

1/4*x <= 0 // : 1/4

x <= 0/1/4

x <= 0

17*x-4 <= 0

17*x-4 <= 0

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

17*x <= 4 // : 17

x <= 4/17

x in (4/17:+oo)

log(x/4)(17*x-4) = 2 // - 2

log(x/4)(17*x-4)-2 = 0

log(x/4)(17*x-4)-2 = 0 // + 2

log(x/4)(17*x-4) = 2

log(x/4)(17*x-4) = log(x/4)((x/4)^2)

17*x-4 = (x/4)^2

17*x-(x/4)^2-4 = 0

17*x-1/16*x^2-4 = 0

DELTA = 17^2-(-4*(-1/16)*4)

DELTA = 288

DELTA > 0

x = (288^(1/2)-17)/(-1/16*2) or x = (-288^(1/2)-17)/(-1/16*2)

x = -8*(12*2^(1/2)-17) or x = -8*(-12*2^(1/2)-17)

x in { -8*(12*2^(1/2)-17), -8*(-12*2^(1/2)-17) }

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