5ln(x^1/2)+ln(9x)

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Solution for 5ln(x^1/2)+ln(9x) equation:


D( x )

9*x <= 0

(x^1)/2 <= 0

9*x <= 0

9*x <= 0

9*x+0 <= 0 // - 0

9*x <= 0 // : 9

x <= 0/9

x <= 0

(x^1)/2 <= 0

(x^1)/2 <= 0

x/2 <= 0

1/2*x+0 <= 0 // - 0

1/2*x <= 0 // : 1/2

x <= 0/1/2

x <= 0

x in (0:+oo)

5*ln((x^1)/2)+ln(9*x) = 0

5*ln(x/2)+ln(9*x) = 0

ln(1*(x/2)^5)+ln(9*x) = 0

ln(1*9*x*(x/2)^5) = 0

ln(9*x*(x/2)^5) = 0

ln(9*x*(x/2)^5) = ln(e^0)

9*x*(x/2)^5 = e^0

9*x*(x/2)^5-e^0 = 0

9/32*x^6 = 1 // : 9/32

x^6 = 32/9

x^6 = 32/9 // ^ 1/6

abs(x) = (32/9)^(1/6)

x = (32/9)^(1/6) or x = -(32/9)^(1/6)

x in { -(32/9)^(1/6)}

x = (32/9)^(1/6)

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