Question

if 2^x=3^y=6^-z ,1/x+1/y+1/z is

Answer 1

let 2^x=3^y=6^-z=k

then 2^x=k

applying logarithm on both sides

xlog2=logk

x=logk/log2

1/x=log2/logk -------------(1)

now ,3^y=k

applying logarithm on both sides...

ylog3=log k

y=logk/log3

1/y=log3/logk------------(2)

now ,6^-z=k

applying logarithm on both sides,

-zlog6=log k

z= -logk/log 6

1/z= -log6/logk ---------(3)



now (1)+(2)+(3) gives


1/x+1/y+1/z =log2+log3-log6 /k

by product law

log 6-log6/k

=o


I hope this will help u ;)