I'm stuck on a pre-calc problem. I need to find y as a function of x, where the constant c is a positive number for In(y-1)+In(y+1)= -x+c
express your question as
ln[(y-1)(y+1)] = -x+c
change that to exponential form
e^(-x+c) = (y-1)(y+1)
e^(-x+c) = y^2 - 1
y^2 = e^(-x+c) + 1
y = ± sqrt(e^(-x+c) + 1)
To solve this pre-calculus problem and find the function y as a function of x, you start by rearranging the given equation.
1. Start with the equation ln[(y-1)(y+1)] = -x + c.
2. Rewrite this equation in exponential form by using the fact that ln(x) = y is equivalent to e^y = x.
In this case, we can rewrite ln[(y-1)(y+1)] as e^(-x+c).
So, the equation becomes e^(-x+c) = (y-1)(y+1).
3. Simplify the equation by multiplying (y-1)(y+1) together.
This gives us e^(-x+c) = y^2 - 1.
4. Isolate y by adding 1 to both sides of the equation.
The equation now reads e^(-x+c) + 1 = y^2.
5. Finally, take the square root of both sides of the equation.
Since we're looking for y as a function of x, we need to consider both the positive and negative square root.
Therefore, we have y = ± sqrt(e^(-x+c) + 1).
This will give you the function y as a function of x.