express as a function. c is a positive number
ln y= 1n x + 1n C
Make both sides of the equation an exponent of e. Remember that x^a * x^b = x^(a+b)
To express the given equation as a function, we need to eliminate the natural logarithm on the left side of the equation. We can do this by raising both sides of the equation to the power of the base, which in this case is the constant "e".
So, let's raise both sides of the equation to e:
e^(ln y) = e^(ln x + ln C)
By the property of logarithms, the exponents can be written as a product:
y = e^(ln x) * e^(ln C)
Since e^(ln x) is equal to x and e^(ln C) is equal to C since they are inverse operations:
y = x * C
Therefore, the expression of the given equation as a function is y = Cx, where C is a positive number.