Question

If
$2 {}^{x} = 3 {}^{y} = 6 {}^{z}$
show that
$\frac{1}{z} = \frac{1}{y} + \frac{1}{x}$
fast with clear steps

Answer 1

$2 {}^{x} = 3 {}^{y} = 6 {}^{z}$

xlog2 = ylog3 = zlog6

x = z log6 / log2

y = z log6 / log3

Now,

1/x + 1/y .

= log2 / zlog6 + log3 / zlog6

= log2 + log3 / zlog6

= log6/zlog6

= 1/z

Hence proved!