Question

if zyz is not equal to 0, 2^x = 3^y = 12^z. Show that (2/x)+(1/y)-(1/z) = 0

Answer 1

pleasee!!

Answer 2

i am not sure whether this'll work but did you try to take log throughout of
2^x=3^y=12^z
?

Answer 3

yes.., i did, but i didn't get solution

Answer 4

Find the common denominator.

Answer 5

i am trying
x log 2 = y log 3 = z(2log 2 +log 3)

y = (x log 2/log 3 )
z = (x log 2)/ ( 2 log 2+ log3)

1/y = log 3 / x log 2
1/z = (2 log 2+log 3) / (x log 2)

1/x [2 + (log 3 - 2 log 2 - log 3 / log 2 ]

i am getting it = 0
why are you not getting ? show your steps ?

Answer 6

yess.., you are.., thanks for helping me., check this one please
http://openstudy.com/study#/updates/528a37f2e4b087edf62bc2ed

Answer 7

alternative :
let 2^x = 3^y = 12^z = k

2^x = k ------> x = log_2 k
3^y = k ------> y = log_3 k
12^z = k -----> z = log_12 k

2/x + 1/y - 1/z
= 2/log_2 k + 1/log_3 k - 1/log_12 k
= 2log_k 2 + log_k 3 - log_k 12
= log_k 2^2 + log_k 3 - log_k 12
= log_k (2^2 * 3) - log_k 12
= log_k 12 - log_k 12
= 0