Question

How do you solve `x ^ 2 - ln x = ln 18 - 6`?

Answer 1

There is no real solution.

Explanation:

The equation can rearranged to the form
`ln (18 x)=x^2+6`

So, `18 x = e^(x^2+6)=e^6s^(x^2)=403.43 e^(x^2)`, nearly.#.

Draw the graphs for y = 18 x and `y = 403.43e^(x^2)`.

The first is a straight line through the origin with slope 18, running from the fourth to the first quadrant.

The second is exponential and asymptotic to y = 0, and is raising from y-axis at `x = -oo`, in the second quadrant, entering the first quadrant through A(0, 403.43). At A, the slope is 403.43, never to meet y = 18 x.
So, there is no solution. .