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.