Logarithms math problem?

Question

Timmins created a mathematical model relating demand and supply of water in Delano, California. According to his model,

p= 1187 - 133 ln x , where p is in dollars and x is in acre feet. Find the demand if p is $800.

Answer 1

I think your confusion is because of the ln x part. But in fact it is a simple equation. Let's say Y = ln x. If we can find a value for Y, then maybe we can calculate X, so that Y = ln X.

If you replace ln x in the original formulat with Y you get:

$800 = 1187 - 133 Y, you should already have learned how to solve this: 133 Y = 1187 - 800 = 387 ==> Y = 387 / 133

Now you know:

ln x = Y = 387 / 133

If you remember the definition of ln x, then it has something to do with  the inverse of a power of e. Or to be exact:

a = ln b if e^b = a

Use this in your equation by making the left and the right a power of e:

e^(ln x) = e^Y = e^(387/133)

e^(ln x) = x, so the answer is x = e^(367/133)