Question

if
$2^{x} = 3^{y} = 12^{z}$
show that
$\frac{1}{z} = \frac{1}{y} + \frac{2}{x}$

Answer 1

) 2^x=3^y=6^z
3logy = zlog6
y = zlog6/log3

xlog2 = ylog3
xlog2 = zlog6log3/log3
x = zlog6/log2

1/x + 1/y = log3/zlog6 + log2/zlog6
= log(3*2)/zlog6
= log6/zlog6
=1/z

so 1/x + 1/y = 1/z