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

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if a^x=b, b^y=c and xyz=1, prove c^z=a
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Amelia 5 months 2021-12-29T17:24:22+00:00 1 Answer 0 views 0

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  1. Eden
    0
    2021-12-29T17:25:46+00:00
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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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