# Thread: find the number of solution of this ln equation

1. you are correct it will be negative for every X.

so its a maximum point

so the derivative before point x=1/a is positive
ans the derivative after point x=1/a in negative.
by i cant see where we got two negative point with a poisitive point in the middle
??

2. Originally Posted by transgalactic
you are correct it will be negative for every X.

so its a maximum point

so the derivative before point x=1/a is positive
ans the derivative after point x=1/a in negative.
by i cant see where we got two negative point with a poisitive point in the middle
??
i dont know how to get it??

3. Originally Posted by transgalactic
i dont know how to get it??
Let's consider a simple example $\displaystyle y = 1 - x^2$. Now it's maximum is located at x = 1 and it's 1 (>0). As $\displaystyle x \to \pm \infty$ then $\displaystyle y \to - \infty$ so there must be two places (at least) where y = - #, one for x > 0 and one for x < 0. In this case, I'll choose $\displaystyle x = -2,\; \text{and}\; x = 3$ where $\displaystyle f(-2) < 0,\; \text{and}\; f(3) < 0$. Better?

4. $\displaystyle y=1-x^2$
$\displaystyle y'=-2x$
y'=0 => x=0
max(0,1)
ahh

so if our highest point is at x=1
then there are two values as x-+->infinty which are negative

5. if
$\displaystyle a < \frac{1}{e}$
then we have two solution

what if it equals 0??

there is no place for being between negative and positive
how do you say that there is 1 solution in that case
??

and
lim ln(x)-ax=+infinity-+infinity
x->+infinity

its not -infinity like you said
??

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