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Question Number 72496 by Shamim last updated on 29/Oct/19

$$\mathrm{if}{\mathrm{a}}^{\mathrm{x}}=\mathrm{b},{\mathrm{b}}^{\mathrm{y}}=\mathrm{c},{\mathrm{c}}^{\mathrm{z}}=\mathrm{a}\mathrm{then}\mathrm{prove}\mathrm{that},$$$$\mathrm{xyz}=0.$$

Answered by som(math1967) last updated on 29/Oct/19

$$a^x=b\Rightarrow a^{xy}=b^y$$$$a^{xy}=c\Rightarrow a^{xyz}=c^z$$$$\therefore a^{xyz}=a\therefore xyz=1$$$$soIthinkitshouldbexyz=1$$

Answered by Tanmay chaudhury last updated on 29/Oct/19

$$a=c^z$$$$a={\left(b^y\right)}^z=b^{yz}$$$$a={\left(a^x\right)}^{yz}=a^{xyz}\to soxyz=1$$

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