Question

Express y in terms of x. Your answer will be a formula y = ... with x in the right-hand side.

1. ln e​​​​​​​² + ln x + ln y = 0

Answer 1

To express y in terms of x in the given equation, we can use the properties of logarithms to simplify and rearrange the equation.

Step-by-step explanation:

To express y in terms of x in the given equation, we need to isolate y on one side of the equation. We can use the properties of logarithms to simplify the equation:

1. Combine the logarithms using the property ln(xy) = ln(x) + ln(y).
2. Apply the property ln(e^2) = 2 to simplify ln(e^2).
3. Move ln(x) and ln(y) to the other side of the equation.
4. Simplify the equation by taking the exponent of both sides, which cancels out the ln function.
5. Finally, solve for y by rearranging the equation.

The final formula for y in terms of x is:

y = e^(-2) / x