Question

if a^x=b, b^y=c and xyz=1, prove c^z=a
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Answer 1

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Answer:

$c^z=a$

Step-by-step explanation:

$Given,a^x=b,b^y=c,xyz=1.$

We need to prove $c^z=a$

$b^y=c$

Now sub. $a^x$ in place of b.

$=>(a^x)^y=c\\\\=>a^{xy}=c$

From xyz = 1 , xy = 1/z

sub. xy = 1/z in $a^{xy}=c$

$=>a^{\frac{1}{z} }=c$

Now powering on both sides by 'z'.

$=>a^{\frac{z}{z} }=c^z\\\\=>a=c^z\\\\=>c^z=a$

Hence Proved.

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