log(27)(x^2-8x)=2/3

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Solution for log(27)(x^2-8x)=2/3 equation:


D( x )

x^2-(8*x) <= 0

x^2-(8*x) <= 0

x^2-(8*x) <= 0

x^2-8*x <= 0

x^2-8*x <= 0

DELTA = (-8)^2-(0*1*4)

DELTA = 64

DELTA > 0

x = (64^(1/2)+8)/(1*2) or x = (8-64^(1/2))/(1*2)

x = 8 or x = 0

a = 1

a > 0

x in <0:8>

x in (-oo:0) U (8:+oo)

log(27)(x^2-(8*x)) = 2/3 // - 2/3

log(27)(x^2-(8*x))-(2/3) = 0

log(27)(x^2-8*x)-2/3 = 0

log(27)(x^2-8*x)-2/3 = 0 // + 2/3

log(27)(x^2-8*x) = 2/3

log(27)(x^2-8*x) = log(27)(27^(2/3))

x^2-8*x = 27^(2/3)

x^2-8*x-27^(2/3) = 0

x^2-8*x-9 = 0

DELTA = (-8)^2-(-9*1*4)

DELTA = 100

DELTA > 0

x = (100^(1/2)+8)/(1*2) or x = (8-100^(1/2))/(1*2)

x = 9 or x = -1

x in { -1, 9 }

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