Question 282424
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?