Question

am i supposed to get a number or an expression in the end? i'm getting an expression so far.... help please! :D

log(10000x/yz)=3 where log_z(y)=1/(logx)

Answer 1

i tried it but couldnt get the answer sorry

Answer 2

In the second expression what is the base? is that z?

Answer 3

@satellite73 @.Sam. @TuringTest @Coolsector @estudier ???

Answer 4

is that an answer or what is that dydif?

Answer 5

OH LET ME TYPE IT AGAIN

Answer 6

wait... http://ateneomathsociety.com/wp/wp-content/uploads/wppa/282.jpg i'm not sure right now... is it base x or z for the 2nd expression??

Answer 7

a question dydif how do you do that where the names are like that where when you go over it it tells them there profile and stuff whenever i try it just looks normal

Answer 8

you put an "@" sign before the username:)

Answer 9

let me try

Answer 10

@dydlf

Answer 11

@ash2326

Answer 12

it worked thanks

Answer 13

@helder_edwin

Answer 14

i got to try this more often

Answer 15

sorry guys! i have an exam tomorrow so yeah... been bothering lots of you tonight! :(

Answer 16

ok

Answer 17

which one is it?

Answer 18

I think it's a z

Answer 19

actually I better not guess, the problem changes a lot depending on whether it's an x or z

Answer 20

@helder_edwin #2 letter d :D

Answer 21

when i solved it i assumed it's a z hahaha maybe we can start with that?:))

Answer 22

\[ \large \log\frac{10000x}{yz}=3 \]
\[ \large 10^3=\frac{10^4x}{yz} \]
\[ \large yz=10x \]
\[ \large x=\frac{yz}{10} \]

Answer 23

which renders the second piece of info useless, so I am confused

Answer 24

@dydlf we get the answer in terms of z or y. Not number.

Answer 25

@helder_edwin thanks!! i didn't look at it that way! i did some crazy log stuff 'cause i got confused with the second piece of info like what @TuringTest said.

hmmm......

Answer 26

you think it's just that, @helder_edwin ? you didn't do anything wrong i believe anyway?

Answer 27

\[ \large \frac{\log y}{\log z}=\log_zy=\frac{1}{\log x} \]
\[ \large \log x=\frac{\log z}{\log y} \]
\[ \large x=10^{\log z/\log y}=(10^{\log z})^{1/\log y}=
z^{1/\log y} \]

Answer 28

We can express in terms of z or y but not in terms of both variables.

Answer 29

so what should the answer be? hahaha x is equivalent to a lot=)) oh weeel hahaha

Answer 30

\[ \large x^{\log y}=z \]

Answer 31

therefore
\[ \large x=\frac{yz}{10}=\frac{y\cdot x^{\log y}}{10} \]

Answer 32

i don't think we can go any further.

Answer 33

\[ \large \frac{10}{y}=x^{\log y-1} \]

Answer 34

\[ \large x=(10/y)^{1/(\log y-1)} \]

Answer 35

this is the best i can get.

Answer 36

maybe the base of the second logarith (which i cannot read clearly) is not z !

Answer 37

i hope it was helpful

Answer 38

if it weren't z... then that means logy=1 right?? since it's logy/logx=1/logx? and yes it was really hepful!!

Answer 39

@dydlf Ok, the answer is x = 1/10
I type how if you don't get it

Answer 40

From \[\log \frac{ 10000x }{ zy }=3\] we get that\[x=\frac{ zy }{ 10 }........(1)\] Now From\[\log_{z}y=\frac{ 1 }{ \log x }\] we will develop this:\[\frac{ \log y }{ \log z }=\frac{ 1 }{ \log x } ...... but - x=\frac{ zy }{ 10 }\]\[\frac{ \log z }{ \log y}=\log x = \log (\frac{ zy }{ 10 })\]\[\frac{ \log z }{ \log y }=\log z + \log y-\log10\]\[\frac{ \log z }{ \log y }-\log z=\log y -1\]\[\log z(\frac{ 1 }{ \log y }-1)=\log y-1\]\[\log z(\frac{ 1-\log y }{ \log y })=\log y -1\]\[\log z=\frac{ \log y-1 }{ \frac{ 1-\log y }{ \log y } }\]\[\log z=\frac{ -(1-\log y) }{ \frac{ 1-\log y }{ \log y } }\]\[\log z =- \log y\]\[\log z = \log y^{-1}\]\[z =\frac{ 1 }{ y }\]\[zy=1 ..........(2)\]INSERTING EQUATION 2 IN 1\[x=\frac{ zy }{ 10 }=\frac{ 1 }{ 10 }\]

Answer 41

@dydlf

Answer 42

wowowowowowow!!!

Answer 43

thank you so much!! that took a lot of effort to type too! thank you!

Answer 44

well come