SOLUTION: Solve the following logarithmic. if there is no solution, state No Solution (Round your to 4 decimal places) ln(x+5)-ln(x-4)=ln(x-2)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve the following logarithmic. if there is no solution, state No Solution (Round your to 4 decimal places) ln(x+5)-ln(x-4)=ln(x-2)      Log On


   

Question 382190: Solve the following logarithmic. if there is no solution, state No Solution (Round your to 4 decimal places)
ln(x+5)-ln(x-4)=ln(x-2)
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
ln(x+5)-ln(x-4)=ln(x-2)
-
ln[(x+5)/(x-4)] = ln(x-2)
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(x+5)/(x-4) = x-2
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x+5 = x^2-6x+8
x^2 -7x + 3 = 0
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x = [7 +- sqrt(49-4*1*3)]/2
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x = [7 +- sqrt(37)/2
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x = (7+sqrt(37))/2 or x = (7-sqrt(37))/2
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x = 6.5414... or x = 0.4586...
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Only Viable Answer: x = 6.5414
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Why? ln(x-2) would be the ln of a negative
if x = 0.4586.
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Cheers,
Stan H.