Expess y as a function of x. C is a positive number.

1n y= 3x + ln C

Make both sides of the equation powers of e.

To make both sides of the equation powers of e, we can use the exponentiation property of logarithms.

1. Start with the equation:
ln y = 3x + ln C

2. Apply the exponentiation property to both sides of the equation:
e^(ln y) = e^(3x + ln C)

3. Rewrite the left side using the inverse relationship between the exponential function (e^x) and natural logarithm (ln x):
y = e^(3x + ln C)

4. Applying the exponentiation property, we can rewrite the right side of the equation:
y = e^3x * e^(ln C)

5. Simplify the expression by using the property that e^(ln C) is equal to C:
y = e^3x * C

Therefore, y can be expressed as a function of x as:
y = C * e^(3x)