Question

ln(x-3)-ln x=1.5

Answer 1

i need to find the value of x

Answer 2

Your first step would be to simplify the LHS as follows:\[\ln(x - 3) - \ln(x) = \ln \left(\dfrac{x - 3}{x}\right)\]

Answer 3

YEs after it ?

Answer 4

Do you know how to remove \(\ln\) from both sides? Raise both sides to the power \(e\).

Answer 5

Yes , i tried to solve this sum , and did it half nd then im stuck ..
I did it this way ,
ln(x-3)/x=1.5
ln(x-3)=1.5x
ln-3=1.5x-x
ln-3=0.5x
and now i dont knw wat to do !!

Answer 6

Hmm, you have to raise both sides to the power of \(e\) because \(\large \frac{x-3}{x}\) is enclosed within \(\ln\).\[\ln\left(\dfrac{x-3}{x}\right) = 1.5\]\[\dfrac{x-3}{x} = e^{1.5}\]

Answer 7

Do you see how and why I did that?

Answer 8

Yes I understand , wat after it ?

Answer 9

\[\dfrac{x -3}{x}=e^{1.5}\]\[x -3 = e^{1.5}x\]\[x - e^{1.5 }x = 3\]\[x(1 - e^{1.5}) = 3\]\[x = \dfrac{3}{1 - e^{1.5}}\]

Answer 10

and then ?

Answer 11

Isn't that it?

Answer 12

no, I need to find out the value of X

Answer 13

That's the value of \(x\).

Answer 14

Ans. should b -0.861

Answer 15

\[\dfrac{3}{1 - e^{1.5}}\]plug this in to your calculator.

Answer 16

oh wow , I got the answer , Thanku so much !!

Answer 17

No problem :)

Answer 18

2lnx4-lnx2 = 12 .

Answer 19

What have you tried?

Answer 20

yes !
lnx4x2-lnx2=12
lnx8-lnx2=12
lnx6=12

Answer 21

Great!

Answer 22

\[6\ln(x) = 12\]\[\ln(x) = 2\]

Answer 23

Oh Ok Thanks !

Answer 24

x4lnx-lnx=0
lnx(x4-1)=0
e(x4-1)=e0
wat aftr it ?