log(8)(2x-3)-log(8)(3x+4)=-1/3

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Solution for log(8)(2x-3)-log(8)(3x+4)=-1/3 equation:


D( x )

3*x+4 <= 0

2*x-3 <= 0

3*x+4 <= 0

3*x+4 <= 0

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

3*x <= -4 // : 3

x <= -4/3

2*x-3 <= 0

2*x-3 <= 0

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

2*x <= 3 // : 2

x <= 3/2

x in (3/2:+oo)

log(8)(2*x-3)-log(8)(3*x+4) = -1/3 // + -1/3

log(8)(2*x-3)-log(8)(3*x+4)-(-1/3) = 0

log(8)(2*x-3)-log(8)(3*x+4)+1/3 = 0

log(8)(1*(2*x-3))-log(8)(3*x+4)+1/3 = 0

log(8)((1*(2*x-3))/(3*x+4))+1/3 = 0

log(8)((1*(2*x-3))/(3*x+4))+log(8)(1*8^(1/3)) = 0

log(8)((1*(2*x-3))/(3*x+4))+log(8)(2) = 0 // - log(8)(2)

log(8)((1*(2*x-3))/(3*x+4)) = -log(8)(2)

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

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

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

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

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

x-10 = 0

(x-10)/(2*(3*x+4)) = 0

(x-10)/(2*(3*x+4)) = 0 // * 2*(3*x+4)

x-10 = 0

x-10 = 0 // + 10

x = 10

x = 10

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