ln X + ln X^2 = 3

Help I'm lost again =/

Also

Log X + Log(x - 21) = 2

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- Jul 24th 2007, 12:27 PMJonathanEyoonLogarithmic Equations Problem
ln X + ln X^2 = 3

Help I'm lost again =/

Also

Log X + Log(x - 21) = 2 - Jul 24th 2007, 12:34 PMCaptainBlack
- Jul 24th 2007, 12:43 PMJonathanEyoon
- Jul 24th 2007, 12:50 PMCaptainBlack
The logarithm property that was the original reason the were invented:

so:

The second logarithm property needed is:

(which is realy just the previous property in disguise),

so:

Therefore we have:

and so:

.

But the number who's log (to any base) is 1 is the base itself, and since we have logs to the base here;

RonL - Jul 24th 2007, 12:53 PMKrizalid
- Jul 24th 2007, 01:33 PMJonathanEyoon
- Jul 24th 2007, 01:34 PMJonboy
You are almost correct Jonathan (hey that's my name too!).

So we have:

Which goes to:

Now raise both to a base of 10:

You can solve the quadratic, make sure to check that both solutions work. - Jul 24th 2007, 01:41 PMJonathanEyoon
- Jul 24th 2007, 01:43 PMJonboy
No prob. Make sure that when you do problem like these you do them step by step and don't rush like me... it'll cause a slight but critical error. Luckily I caught myself. Good luck!

- Jul 24th 2007, 01:47 PMJonathanEyoon
- Jul 25th 2007, 06:17 AMtopsquark