SOLUTION: given,
ln(3y+2)=5ln(x-1)-ln(2-x)-x
1)determine the range of x and y.
2)find y explicitly as a function of x.
thanks.
Algebra.Com
Question 673239: given,
ln(3y+2)=5ln(x-1)-ln(2-x)-x
1)determine the range of x and y.
2)find y explicitly as a function of x.
thanks.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
ln(3y+2)=5ln(x-1)-ln(2-x)-x
1)determine the range of x and y.
Those anti-logs must ALL be positive.
y has to be > -2/3
x has to be greater than 1 but less than 2
----
Domain: All Real Numbers greater than 1 but less than 2
Range: All Real Numbers greater than -2/3
----
2)find y explicitly as a function of x.
ln(3y+2) = ln[(x-1)^5/(2-x)] - x
-----
That looks like a mess but here goes:
---
3y+2 = 10^[ln[(x-1)^5/(2-x)] - x]
----
y = [10^[ln[(x-1)^5/(2-x)] - x]- 2]/3
=============================================
Cheers,
Stan H.
================
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