Question 76

If $$a = 2^x, b = 4^y, c = 8^z$$ and $$a^{yz} . b^{zx} . c^{xy} = 4^6$$, then $$xyz = ...........$$

Solution

given that

$$a = 2^x, b = 4^y, c = 8^z$$ and

$$a^{yz} . b^{zx} . c^{xy} = 4^6$$ put the value of a,b and c

$$ 2^{xyz} . 4^{yzx} . 8^{zxy} = 4^6$$

$$ 2^{xyz} . 4^{yzx} . {2$$\times$$4}^{zxy} = 4^6$$

$$ 4^{xyz} . 4^{yzx} . 4^{zxy} = 4^6$$

$$ 4^{3zxy} = 4^6$$ when base are same then power will be equal

3xyz = 6

xyz = 2 Answer

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