Question

Number of positive soluion which satisfy this equation

Answer 1

\[\log_{2}x.\log_{4}x.\log_ {6}x=\log_{2}xlog_{4}x+\log_2{x}\log_{6}x+\log_{4}xlog_{6}x \]

Answer 2

@ganeshie8 @hartnn @ParthKohli @nincompoop hlp

Answer 3

multiply throughout by log 2 log 4 log 6

Answer 4

use this :
\(\huge \log_ab = \dfrac{\log b}{\log a}\)

Answer 5

then multiply throughout by log 2 log 4 log 6 and you will see (log x)^2 getting cancelled from both sides,
and all that remains is
log x = log 2+ log 4+log 6 = log (48)

Answer 6

oh and since you are cancelling log x from both sides,
log x cannot be 0

when log x is 0, x= 1 is another integer solution.

Answer 7

in all, total 2