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BabaBlast [244]
3 years ago
12

If a = b^c b=c^a and c =a^b prove abc =1​

Mathematics
1 answer:
alekssr [168]3 years ago
5 0

Answer:

Step-by-step explanation:

a = b^{c}   ------------(I)

Plug in b = c^{a}

(I) ---> a = (c^{a})^{c}= \ c^{a*c} = \ c^{ac}    -----------(II)

Plug in c = a^{b}

(II) ----->

 a = (a^{b})^{ac} \\\\a = a^{ac*b}\\\\a = a^{abc}

Both sides base are same. So, compare the powers

1 = abc

abc = 1

Hence proved

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