Question

It is given that ln(y+1) - lny = 1 +3lnx. Express y in terms of x, in a form not involving logarithms.

Answer 1

@3mar

Answer 2

What I have so far is: ln(y+1) - lny = lne + 3lnx

Answer 3

Can you try firstly yourself?

I am with you if you stuck!

Answer 4

Is it possible to cancel out all of the lns? Or am I just thinking very off? >.<

Answer 5

Oh, that wouldn't work, because it would cancel out the y. Yikes.

Answer 6

Should I do something with ln(y+1)?

Answer 7

Like distribute it?

Answer 8

You can't as there are operations between them
Only you can if there are like that\[\ln(ffremlkfergknrel)=\ln(fewferfiop$Y%$)\]
then
\[ffremlkfergknrel=fewferfiop$Y%$\]

Answer 9

We are trying to isolate y, correct?

Answer 10

So, I would e both sides?

Answer 11

No, you would firstly do that:
\[\ln(y+1) - lny = 1 +3lnx.\]
\[\ln[\frac{ y+1 }{ y }]= 1 +3lnx\]

agree?

Answer 12

OH because subtraction is division.

Answer 13

Excellent!

Answer 14

http://www.wolframalpha.com/input/?i=(y%2B1)+-+lny+%3D+1+%2B3lnx

Answer 15

Then it would better to do that
\[\ln[\frac{ y+1 }{ y }]= 1 +3lnx\]
then
\[\ln[\frac{ y+1 }{ y }]-3lnx=1\]
then
\[\ln[\frac{ y+1 }{ y }]-lnx^3=1\]
then
\[\ln[\frac{ y+1 }{ y*x^3 }]=1\]

agree?

Answer 16

Well, I just wrote down the 3rd thing you had so I guess I agree. :o

Answer 17

Great!

Now you can eliminate the ln by doing that
\[\ln[\frac{ y+1 }{ y*x^3 }]=1\]
then
\[\ln[\frac{ y+1 }{ y*x^3 }]=\ln(e)\]
then
\[\frac{ y+1 }{ y*x^3 }=e\]
then
\[ y+1=e* y*x^3\]
then
\[ y+1=e*x^3*y\]
then
\[ y-e*x^3*y=-1\]
then
\[ y(1-e*x^3)=-1\]
then
\[\Huge y=\frac{ -1 }{ (1-e*x^3) }\]

Answer 18

Do you have any difficulties?

Answer 19

Let me check my work. I got that answer though.

Answer 20

Alright, all my steps were closely the same as yours so I got that too. That's it for it?

Answer 21

Do you need any more simplicity than this? ;]

Answer 22

@Vuriffy

Satisfied?

Answer 23

A little confused, http://www.wolframalpha.com/input/?i=ln(y%2B1)+-+lny+%3D+1+%2B3lnx says the answer would be: y = 1/(ex^3 - 1)

Answer 24

Should the y be negative at any point, because if it was then you would multiply each side by -1 and it would equal that.

Answer 25

Ahh, they equal the same don't they?

Answer 26

\[\Large y=\frac{ -1 }{ (1-e*x^3) }=\frac{ +1 }{ (-1+e*x^3) }=\frac{ +1 }{ (e*x^3-1) }\]

HAPPY NOW?

Answer 27

Haha, yes. Thank you so much. (:

Answer 28

Thank you for learning!

Good learner! I really like who ask and stop the explanation when he sticks to something, even it looks so simple!

Any more questions?

Answer 29

No, I am fine now! I appreciate it.