math help (logs)

Not sure how to handle this problem. Any help would be appreciated.

ln^2(X) + ln(X)^3 + 2 = 0

In the first term the exponent is with the natural log. In the second term the exponent is with the X value.

I know it can be written like this:

ln^2(X) + 3ln(X) + 2 = 0

But I don't know how to deal with the first term.

If it helps, the answers are supposed to bex=e^-1orx=e^-2.

yeah, it definitely does factor. I think the squared log on the first term can be viewed as the first term of a polynomial to the second power...so i'm going with something like:

let ln^2(X) = t^2
let ln(X)^3 = 3t

and rewrite:
t^2+3t+2=0
(t+1)(t+2)=0

t=-1 or -2

Now I'm wondering if there is a more direct way to deal with the natural log form...

Noodlemod_sl said:

So for the first factor;:

1+ln(x) = 0 OR ln(x) = -1

Then

e^(ln(x)) = e^(-1)

x = e^(-1)


For the second same thing:
e^(ln(x)) = e^(-2)

e^(lnx)) = x is the golden rule

Click to expand...

definitely! thank you.