Express y as a function of x. The constant C is a positive number.
ln y = ln x + ln C
To express y as a function of x, we can start by using the properties of logarithms.
We have the equation:
ln y = ln x + ln C
First, let's simplify the right-hand side of the equation by using the property of logarithms that states ln(a) + ln(b) = ln(a*b):
ln y = ln (x * C)
Now, we can exponentiate both sides of the equation with the base e, which is the inverse function of the natural logarithm:
e^(ln y) = e^(ln (x * C))
Remember that e^(ln a) cancels out the logarithm, leaving you with just a:
y = x * C
Therefore, we can express y as a function of x:
y(x) = Cx
So, y is a linear function of x, with the constant C determining the slope of the line.