SOLUTION: What is the value of x? 0.5 ln (110-x)+0.5 ln (100-x) = 4.26 0.8 ln (200-x) + 0.2 ln (100-x) = 4.56

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: What is the value of x? 0.5 ln (110-x)+0.5 ln (100-x) = 4.26 0.8 ln (200-x) + 0.2 ln (100-x) = 4.56      Log On


   

Question 282424: What is the value of x?
0.5 ln (110-x)+0.5 ln (100-x) = 4.26
0.8 ln (200-x) + 0.2 ln (100-x) = 4.56
Answer by dabanfield(803) About Me  (Show Source):
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1.) 0.5 ln (110-x)+0.5 ln (100-x) = 4.26
2.) 0.8 ln (200-x) + 0.2 ln (100-x) = 4.56
1.) .5 ln(110-x) + .5 ln(100-x) = 4.26

.5*(ln(110-x)+ ln(100-x)) = 4.26
ln(110-x) + ln(100-x) = 4.26/.5
Using the law ln a + ln b = ln (a+b):
ln((110-x)*(100-x)) = 8.52
By definition of ln we have:
(110-x)*(100-x) = e^8.52
Solve the above for x using the quadratic formula.
2.) 0.8 ln (200-x) + 0.2 ln (100-x) = 4.56
Are you sure the equation above is written correctly?