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

1 Answer
A. S. Adikesavan
Apr 15, 2016

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. .

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