Question 76

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

Solution
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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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