Question

Given 2 power x = 3 power y = 6 power p , show that p = xy/ x+y. Obviously this is a logarithm question.

Answer 1

so the question is '

\[\large 2^x=3^y=6^p\]

Answer 2

noted

Answer 3

ok taking logarithm

\[x \log 2=y \log 3=p \log 6\]

Answer 4

yea right that was what you told me to learn which is the basics i did that

Answer 5

logarithm as the required solution?

Answer 6

no show that p = xy/ x+y

Answer 7

now log(6)=log 3+log 2

Answer 8

understood that.

Answer 9

The confusing part should be somewhere after this steps.

Answer 10

which i'm stuck.

Answer 11

wait a sec pls i am doing on paper

Answer 12

@Sgstudent i also got stuck :( ...lets see if sirm3d can help :)

Answer 13

i'll post a non-logarithm solution.
\[\Large{2^x=6^p\\(2^x)^y=(6^p)^y\\2^{xy}=y^{py}}\]

Answer 14

that's \[\Large 2^{xy}=6^{py}\]

Answer 15

lol i need to use logarithm to solve this type of question is going to be out in my upcoming class test this thursday.

Answer 16

ok got it !!

Answer 17

:)

Answer 18

ahhh. you wan't logarithm solution.
\[x\log2=p\log6\\xy\log2 = py\log 6\\y\log 3 = p\log 6\\xy\log 3 = px\log 6\]

Answer 19

add the equations:
\[\Large xy\log 2 + xy\log 3 = py\log 6 + px\log 6\]

Answer 20

from my 2nd step

\[\large \dfrac{y}{x}=\dfrac{\log 2}{\log 3}\]

Answer 21

I will review both solutions and see which i can understand easier.

Answer 22

\[\Large {xy\log 6 = \log 6 (py + px)\\xy=p(y+x)\\\frac{xy}{x+y}=p}\]

Answer 23

oh sirm3d can you compile all your workings into one?

Answer 24

easier to refer to thanks

Answer 25

ok

Answer 26

i think AravindG method will be much longer.

Answer 27

Thank you for the effort.

Answer 28

now

\[p(\log3+\log 2)=y \log 3 \]

divide by \(\log 3 +\log 2 \) on both sides

\[p=\dfrac{y \log3}{\log 3+\log 2}\]

divide by log 3 on both numerator and denominator

\[p=\dfrac{y}{{1+ (\dfrac{\log 2}{\log 3}}}\]

Answer 29

substitute

\[\dfrac{\log 2 }{\log 3}=\dfrac{y}{x}\]

and yu will get the answer :)

Answer 30

lol i'm amazed

Answer 31

amazed?

Answer 32

this question took my class about 50 mins to solve and came out with the solution you mentioned/

Answer 33

1st equation\[\Large{2^x=6^p\\x\log2 = p\log6}\]multiply both sides by y\[\Large xy\log 2 = py\log 6\]

2nd equation:\[\Large {3^y=6^p\\y\log3=p\log6\\xy\log 3 = px\log 6}\]

add the two equations\[\Large{xy\log 2 + xy\log 3 = py\log 6 + py\log 6\\xy(\log 2 + \log 3)=p(x+y)\log 6\\xy\log 6=p(x+y)\log 6 \\\frac{xy\log 6}{(x+y)\log 6}=p\\\frac{xy}{x+y}=p}\]

Answer 34

@Sgstudent who mentioned ?

Answer 35

you

Answer 36

:)

Answer 37

but i did not copy down the solution i prefer something simpler

Answer 38

hence, i decided to come here and look for the solution i want :P

Answer 39

now you have two different solutions. ;-)

Answer 40

:) all the best ..happy to know that you learned the basics :)

Answer 41

thanks both of you

Answer 42

yw :)

Answer 43

i know why you multiply y in the first equation it is because p(x+y) = px+py am i right?

Answer 44

this is called deduction method i suppose

Answer 45

i need to add xlog 2 and y log 3 and combine as one term. hence it can only be done if they have the same literal coefficients, xy.

Answer 46

noted.

Answer 47

AravindG

Answer 48

http://openstudy.com/study#/updates/5103f56be4b0ad57a562ff25

Answer 49

please help if possible :)

Answer 50

I need some tips on delivering a speech without a script etc.