Express y as a function of x. The constant C is a positive number.
ln y = 9x + ln C
To express y as a function of x, we need to eliminate the natural logarithm (ln) on the left side of the equation.
Start by using the property of logarithms that states ln(a) + ln(b) = ln(a * b). We can apply this property to rewrite the equation as:
ln y = ln (Ce^9x)
Next, we can use the fact that ln(e^z) = z to simplify further:
ln y = 9x + ln C
Now, exponentiate both sides of the equation with the base e (which is the inverse function of ln), so we get:
e^(ln y) = e^(9x + ln C)
This simplifies to:
y = e^(9x) * e^(ln C)
Remember that e^(ln C) is equal to C since the exponential function e^x is the inverse function of ln(x).
Therefore, the expression for y as a function of x is:
y = Ce^(9x), where C is a positive constant.