Question

Logaritm Question!!!

Answer 1

Find a relation between x and y that does NOT involve logarithms:
log x + log y = log (x+ y)

Answer 2

Can we assume it's a log of base 10?

Answer 3

yes i think so

Answer 4

logx + log y is never log(x+y) it seems... it is log(xy)

Answer 5

do you want the answer?

Answer 6

I suppose we could exponentiate both sides..
\[\huge 10^{(\log x + \log y)}=10^{\log(x+y)}\]
Using rules of exponents we can split up the left side like this:
\[\huge 10^{\log x}*10^{\log y}=10^{\log(x+y)}\]
Recognizing that log base 10, and the exponentiation base 10 are inverse operations of one another, they essentially "cancel out". Giving us:
\[\huge xy=(x+y)\]
\[\huge y=\frac{x}{x-1}\]

Answer 7

Something like that maybe? :o

Answer 8

@zepdrix Oooh, sexy!

Answer 9

lol :3

Answer 10

@zeptr
yes thats the answer !!!

Answer 11

Oh cool. :)

Answer 12

Were you just testing us or something? :D lol
Knew the answer the whole time huh? XD

Answer 13

@AERONIK , it seems that logx+logy=log(x+y) sometimes.
I wouldn't say NEVER.
Obviously it doesn't match the rule for logs that we had in mind.
But if you plug in y=2, x=2 into the original equation, that should work out ok as one solution :D Since 2+2 is the same as 2*2

Answer 14

no i had the answers at the back of book but i have no idea how to do it... i still dont get the logic though...

Answer 15

so it is not an identity and just a function you say ?

Answer 16

yeh just a random equation

Answer 17

Yah it appears it wasn't testing you on whether or not you knew your log identities, they just wanted to see a relationship between x and y. Interesting problem :O

Answer 18

and one more thing in your proof you have assumed the given statement to be correct, can you please give a formal proof for te same?

Answer 19

what now? :o

Answer 20

and is it log to the base 10 or log to the base e ?

Answer 21

For this problem, we have to assume that they are ALL the same base. Otherwise it won't work out the same. If they're a different base, let's say A, then we exponentiate, writing each side with a base A (regardless of what A might be) and it will work out the same! :D

Answer 22

Different than 10 i mean*

Answer 23

oh ok. sorry ..

Answer 24

10 logx ∗10 logy =10 log(x+y) Recognizing that log base 10, and the exponentiation base 10 are inverse operations of one another, they essentially "cancel out". HOW DID YOU DO THIS STEP... CAN YOU SHOW ME? PLEASE

Answer 25

by defination if y=log x to the base a, then x is nothing but a^y, just use this and you can prove the identity.

Answer 26

\[\large \arcsin( \sin x)=x\]\[\huge e^{\ln x}=x\]
Yah this is true of any function and it's inverse :D Remember it in trig with the inverse functions?

Answer 27

no ...can you do a proof for it please?

Answer 28

Hmmm this might be a little confusing.. I drew a lot of arrows :| lemme know if it makes some sense.