No, you can not separate:
ln ( 7 + x ) ≠ ln 7 + ln x
You can separate just if you have a logarithm of multiplication.
For example:
ln ( 7 · x ) = ln 7 + ln x
Answer:

Step-by-step explanation:
I hope I did this right:
So first thing to do is set up the equation.

Next thing to to is subtract 1/3 from both sides to get:

Next up, you will multiply each of the fractions by the opposing value
(multiply 1/8 by 3 and 1/3 by 8)


Alright almost done, by multiplying 24 by 5 you get 120, that will go in the numerator to make the math a lot easier.
K = 

Finally, you subtract 123 over 24 by 8 over 24.
K = 
Then just simplfy the 115/24 to get

The height of the fence is irrelevant. The bottom of the ladder is 3+8 = 11 feet from the building. The window is 14ft above the ground:
sqrt(14^2+11^2) = length of your ladder.
He can drink 2/5 of the 8 3/4 sodas.

The answer is 7/2 or 3 1/2 sodas.
Of course, Fred would be better off is he drank water instead of soda. :-)