Question

if 2powerx=3powery = 6 power-z show that 1 /x+1/y+1/z=0

Answer 1

Let 2^x = 3^y = 1/6^z = k

Take logarithms.

x = Log K base 2.
1/x = Log 2 base k.
y = Log K base 3
1/y = log 3 base k.

z = - log k base 6
1/z = - log 6 base k.

So 1/x + 1/y + 1/z = 0.
Proved