Question

How to show x.y.(ln x) = (ln y) ?
x times y times (ln x) equals to (ln y)

Answer 1

@ganeshie8 @kropot72

Answer 2

so what are we showing?

Answer 3

yxln(x)=ln(y)?

Answer 4

i mean, i dun understand how x.y.(ln x) equals to (ln y)

Answer 5

help please T.T

Answer 6

I don't see how it is true:
Let x=2,y=1
left hand side: 1*2*ln(2)=2ln(2)
right hand side: ln(1)=0
2ln(2) doesn't equal 0

Answer 7

so maybe I don't understand the question

Answer 8

like since xyln(x)=ln(y) is not true for all x,y in the positive real numbers

Answer 9

1/(1- xy(lnx)) = 1/(1 - (lny))

Answer 10

1/[1- (xy(lnx))] = 1/[1 - (lny)]

Answer 11

I would figure you just are finding specific solutions, not actually proving they're equal. So one solution would be x = 1, y = 1
(1)(1)ln(1) = ln(1)
0 = 0

Unless you're looking for solutions like that, the two are definitely not equal for all x and y.

Answer 12

i feel you're not sharing us the complete question @HatcrewS

Answer 13

y = x^(xy). Find dy/dx in terms of x and y. @ganeshie8

Answer 14

Now that makes way more sense.

Answer 15

oh so you mean to differentiate xyln(x)=ln(y) not show they are equal

Answer 16

So you took ln of both sides to get what you had before, but you still needed to differentiate and actually answer the question.

Answer 17

y = x^(xy)
ln y = xy ln x
Differentiate w.r.t x
(1/y) (dy/dx) = (1/x) xy + ln x [ x (dy/dx) + y]
dy/dx (1/y) = y + ln x x (dy/dx) + y lnx

Answer 18

@freckles do you know how to solve ?

Answer 19

put your terms that have y' on one side and the terms that don't y' on the opposite side

Answer 20

i already did that

Answer 21

\[\frac{dy}{dx} \frac{1}{y}=y+x \ln(x) \frac{dy}{dx}+y \ln(x) \\ \frac{dy}{dx} \frac{1}{y}-x \ln(x) \frac{dy}{dx}=y+yln(x)\]

Answer 22

now factor the dy/dx out on the left hand side

Answer 23

i got this

Answer 24

\[\frac{ dy }{ dx } = \frac{ y^{2}(1+lnx) }{ 1-xylnx }\]

Answer 25

\[\frac{dy}{dx}(\frac{1}{y}-x \ln(x))=y+yln(x) \\ \frac{dy}{dx}(\frac{1-xyln(x)}{y})=y+yln(x)\]
so multiply by the reciprocal of what is being multiplied by y'
looks good
you already did it good job.

Answer 26

the answer sheet show it becomes \[\frac{ y ^{2}(1+lnx) }{ 1-lny }\]

Answer 27

which i dont know how

Answer 28

well remember you said xyln(x) was equal to ln(y)

Answer 29

thus i was wondering how xy(lnx) becomes (ln y). it is not given. i simply based off from this.

Answer 30

it was given by you

Answer 31

by you and the problem by what you read from the problem

Answer 32

okay thanks