ln(2t-12)-ln(4t-27)=ln(2t/27)

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Solution for ln(2t-12)-ln(4t-27)=ln(2t/27) equation:


D( t )

(2*t)/27 <= 0

4*t-27 <= 0

2*t-12 <= 0

(2*t)/27 <= 0

(2*t)/27 <= 0

2/27*t+0 <= 0 // - 0

2/27*t <= 0 // : 2/27

t <= 0/2/27

t <= 0

4*t-27 <= 0

4*t-27 <= 0

4*t-27 <= 0 // + 27

4*t <= 27 // : 4

t <= 27/4

2*t-12 <= 0

2*t-12 <= 0

2*t-12 <= 0 // + 12

2*t <= 12 // : 2

t <= 12/2

t <= 6

t in (27/4:+oo)

ln(2*t-12)-ln(4*t-27) = ln((2*t)/27) // - ln((2*t)/27)

ln(2*t-12)-ln(4*t-27)-ln((2*t)/27) = 0

ln(1*(2*t-12))-ln(4*t-27)-ln((2*t)/27) = 0

ln((1*(2*t-12))/(4*t-27))-ln((2*t)/27) = 0

ln(((1*(2*t-12))/(4*t-27))/((2*t)/27)) = 0

ln(((2*t-12)/(4*t-27))/((2*t)/27)) = 0

ln(((2*t-12)/(4*t-27))/((2*t)/27)) = ln(e^0)

((2*t-12)/(4*t-27))/((2*t)/27) = e^0

((2*t-12)/(4*t-27))/((2*t)/27)-e^0 = 0

(2*t-12)/(2/27*t*(4*t-27))-1 = 0

(2*t-12)/(2/27*t*(4*t-27))+(-1*2/27*t*(4*t-27))/(2/27*t*(4*t-27)) = 0

2*t-1*2/27*t*(4*t-27)-12 = 0

4*t-8/27*t^2-12 = 0

4*t-8/27*t^2-12 = 0

4*(t-2/27*t^2-3) = 0

t-2/27*t^2-3 = 0

DELTA = 1^2-(-3*(-2/27)*4)

DELTA = 1/9

DELTA > 0

t = ((1/9)^(1/2)-1)/(-2/27*2) or t = (-(1/9)^(1/2)-1)/(-2/27*2)

t = 9/2 or t = 9

4*(t-9/2)*(t-9) = 0

(4*(t-9/2)*(t-9))/(2/27*t*(4*t-27)) = 0

(4*(t-9/2)*(t-9))/(2/27*t*(4*t-27)) = 0 // * 2/27*t*(4*t-27)

4*(t-9/2)*(t-9) = 0

( t-9/2 )

t-9/2 = 0 // + 9/2

t = 9/2

( t-9 )

t-9 = 0 // + 9

t = 9

t in { 9/2}

t = 9

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