Question

If
$a {}^{x} = b \\ b {}^{y} = c \\ c {}^{z} = a$
then prove
$x \times y \times z = 1$

Answer 1

hope this helps you.......

Answer 2

Hey mate!!!!!

Given
${a}^{x} = b$
so we can write b^y as
$( {a}^{x} ) {}^{y}$
and also given that c^z is a
so we can write
$(({c}^{z} ) {}^{x} ) {}^{y}$
By opening brackets we have

${c}^{zxy}$
now we know that
${a}^{x} = b \\ {a}^{xy} = c$

because b^y = a^xy = c

and also

${a}^{xy} = {c}^{xyz}$
so
${a}^{xy} = {c}^{xyz} = c$
because a ^xy = c

so
now bases are same and c = c^1

so

${c}^{xyz} = {c}^{1}$
now since bases are same we can write
$xyz = 1$

Hope it helps dear friend ☺️✌️✌️