9 replies to this topic

[Random]

So I have a test tomorrow and I realize I have no idea how to do any of this garbage.

For example:
Solve for x, leave in ln or e if applicable:
ln x + ln(x^2 - 9) = ln 9x

or this one

Same directions:
e^2x + e^x - 12 =0

Can anyone help me with these? It would be much appreciated.

[Frank274]

I'm in precalc, and this doesn't make any sense to me.

I'm doing polynomial dividing

[rockage]

We did this in 3-4 last year, evaluating logs and all.

Since it's a natural log (or at least from what I see they are) you know they are base 10, so that should help you out...

[hungryhippo]

We did this in 3-4 last year, evaluating logs and all.

Since it's a natural log (or at least from what I see they are) you know they are base 10, so that should help you out...

that is not right. Natural logs are logs with base e

[rockage]

Ah I meant common log, my mistake.

[Melchoire]

I think I got the 2nd one:

e^2x + e^x - 12 = 0
e^2x + e^x = 12

Take the natural log from both sides:
2xlne + xlne = 12

The natural long of e is 1 so:
2x(1) + x(1) = 12
3x = 12
x = 4

Edited by FlashGM, 17 November 2008 - 08:18 PM.

[Casilla]

The great things about logs is that they have some simple expansion rules!

log(xy) = logx + logy
log(x/y) = logx - logy


ln x + ln(x^2 - 9) = ln 9x

ln(x) + ln(x^2 - 9) = ln(9) + ln(x)

ln(x) cancels out from both sides

ln(x^2 - 9) = ln (9)
ln(x^2 - 9) - ln(9) = 0
ln((x^2 -9)/9) = 0

Now, we know ln(1) = 0, so therefore,

(x^2 - 9)/9 = 1, which means x^2 - 9 = 9, x^2 = 18, so x has to be radical 18 (that is, square root of 18).

And FlashGM got the second one.

[ShadowLink64]

Oh, people beat me to this topic.

EDIT: I agree with Sonya's answer, but I wish to contest FlashGM's.

e^2x+e^x - 12 = 0

Write it in the form of a quadratic equation:
(e^x)²+e^x - 12 = 0

Factor it:
(e^x + 4)(e^x - 3) = 0

Therefore:
e^x = -4
and
e^x = 3

Take the natural logarithm of both sides (the first root is impermissible since ln(-something) does not exist in the domain of ln(x)):

x = ln(-4) << Does not Exist
x = ln(3)

There is your solution... x = ln(3). Try it.

Take the natural log from both sides:
2xlne + xlne = 12

ln(e^2x + e^x) cannot be divided into ln(e^2x) + ln(e^x). Only if there's a product inside your logarithm.

[Zip]

LOL nub.

Keep in mind that e^ln(x) = x
and
ln(e^x) = x

and it's rather simple.

[Random]

Thanks guys I think I did alright on my test even though I admittedly didn't see thse last night