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

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


D( x )

2*x-3 <= 0

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)

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

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

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

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

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

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

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

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

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

2*x = 4^(3/2*(log(8)(2)))+3 // : 2

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

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

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