Question Number 72496 by Shamim last updated on 29/Oct/19
$$\mathrm{if}\:\mathrm{a}^{\mathrm{x}} =\mathrm{b},\:\mathrm{b}^{\mathrm{y}} =\mathrm{c},\:\mathrm{c}^{\mathrm{z}} =\mathrm{a}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}, \\ $$$$\mathrm{xyz}=\mathrm{0}. \\ $$
Answered by som(math1967) last updated on 29/Oct/19
$${a}^{{x}} ={b}\:\Rightarrow{a}^{{xy}} ={b}^{{y}} \\ $$$${a}^{{xy}} ={c}\Rightarrow{a}^{{xyz}} ={c}^{{z}} \\ $$$$\therefore{a}^{{xyz}} ={a}\:\therefore{xyz}=\mathrm{1}\: \\ $$$${so}\:{I}\:{think}\:{it}\:{should}\:{be}\:{xyz}=\mathrm{1} \\ $$
Answered by Tanmay chaudhury last updated on 29/Oct/19
$${a}={c}^{{z}} \\ $$$${a}=\left({b}^{{y}} \right)^{{z}} ={b}^{{yz}} \\ $$$${a}=\left({a}^{{x}} \right)^{{yz}} ={a}^{{xyz}} \rightarrow{so}\:{xyz}=\mathrm{1} \\ $$