9/
09/2014 Express
y
as a function of x
alone. C is a positive number.
3
ln y = ½ ln (2x + 1) – ¼ ln (x + 4) + C
Scroll
down for the solution.
9/09/2014
Solution.
Moving the ln terms to one side:
3
ln y – ½ ln (2x + 1) + ¼ ln (x + 4) =
C
Condensing:
ln y3
– ln√(2x
+ 1) + ln 4√(x
+ 4) = C
→
ln
[y3·4√(x
+ 4) /√(2x
+ 1)]
= C
Switching
to exponential form:
[y3·4√(x
+ 4) /√(2x
+ 1)]
= eC
Cross-multiplying:
y3 = eC·√(2x + 1)/4√(x + 4)
This expression may be left alone as the answer or one may take the cube-root of it.