math help (logs)

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K

koljec_sl

shitlord
845
2
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.
 
Noodleface

Noodleface

A Mod Real Quick
38,268
15,089
you can factor it, does this help? It's been forever since I did stuff with logs

(1+ln(x))(2+ln(x)) = 0
 
K

koljec_sl

shitlord
845
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...
 
Noodleface

Noodleface

A Mod Real Quick
38,268
15,089
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
 
Noodleface

Noodleface

A Mod Real Quick
38,268
15,089
I took so many math courses (some as my electives... what was I thinking
frown.png
), I was only 3 away from a BS or BA in mathematics, can't remember which.
 
Phelps McManus

Phelps McManus

<Silver Donator>
215
144
koljec_sl said:
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
Click to expand...
I think you can start with refactoring to ln(x)^2 + 3 ln(x) + 2 = 0, substitute t = ln(x), and just go straight to the rewrite.
 
Cad

Cad

scientia potentia est
<Bronze Donator>
25,426
49,040
Noodlemod_sl said:
I took so many math courses (some as my electives... what was I thinking
frown.png
), I was only 3 away from a BS or BA in mathematics, can't remember which.
Click to expand...
I did too but it was... a long time ago. And contrary to popular belief you do not use calculus in software development. At least I never did.
 
DickTrickle

DickTrickle

Definitely NOT Furor Planedefiler
13,403
15,563
I have forgotten most of the math I learned and I never used it in the real world. Getting a Computer Science degree prepares you more for further work in academia than the real world, imo.
 
ToeMissile

ToeMissile

Pronouns: zie/zhem/zer
<Gold Donor>
3,159
2,049
Wolfram alpha says to eliminate the quadratic term by substituting x = 1/3 + log(x)
 
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