Help!!!! Urgent!!!!!! Can You Do This Question?????????? (1 Viewer)

[spunkymonkey225]

The question is.

Find all the values of x for which:
ln x = 2 ln x

IVE GOT NOT IDEA
PLEASE SHOW FULL WORKING IF YOU KNOW.
Tristan

 

[Huy]

lnx = 2lnx
lnx = lnx^2; recall clogaB = logaB^c
taking the log(e) of both sides
x = x^2
x^2 - x = 0
x(x-1) = 0
x = 0 or 1

.'. x = 1, as e^x cannot equal 0 for any value of x.

 

[howareya]

e both sides

1= x2

x= -1 x= 1

right?

 

[howareya]

sorry x cannot be negative

therfore x = 1

 

[kewpid]

x can't equal 0 either

 

[Lazarus]

Originally posted by spunkymonkey225
Find all the values of x for which:
ln x = 2 ln x

I think the simplest solution is...

<pre><font size=2>2.ln(x) = ln(x)
ln(x) = 0 subtracting ln(x) from both sides
x = e⁰ rewriting as exponential
.'. x = 1</font></pre>

 

[howareya]

yep your right

 

[lifes_a_slut]

lol.. ok this is unrelated to maths but targeted at lazurus.. OMG ur from Narrabeen!!!!!! i love narrabeen my family used to go there for 2 weeks every xmas at the lakeside caravan park.. its sooooo beautiful awww how i miss it!

theres no point to my msg, just a little excited.. lol

 

[Lazarus]

LOL!

That park is only a few blocks away. I like it too.