SOLUTION: ln(x^2+3x-4)-ln(x+14)=3

Question 1034961: ln(x^2+3x-4)-ln(x+14)=3
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
ln(x^2+3x-4)-ln(x+14)=3
ln(x^2+3x-4) = ln(x+14) + 3 = ln(x+14) + ln(e^3)
ln(x^2+3x-4) = ln(e^3*(x+14))
x^2+3x-4 = e^3*(x+14) = e^3x + 14e^3
x^2 + (3-e^3)x - (4+14e^3) = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1432.70557195361 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 27.4683171455397, -10.3827802223519. Here's your graph:

RELATED QUESTIONS
x= ln 3 + ln 4 - ln... (answered by jim_thompson5910)

ln(x-3)+ln(x)=ln(4) (answered by venugopalramana)

ln x - ln(x-4) =ln... (answered by Fombitz)

ln x+ 2 ln 4 = ln 7- ln... (answered by scott8148)

Solve: log base 4 (X) + Log base 8 (x) = 1 ln X/ln 4 + ln X/ln 8=1 2 ln X/2 ln 4 + ln... (answered by Fombitz)

solve ln(x3) + ln(x^4) =... (answered by Alan3354)

3^ ln x = 3x (answered by Fombitz)

solve:... (answered by dabanfield)

ln(x+3)=ln(6-3x) (answered by hokies)