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Question

If $$\displaystyle 64 = x^{y}$$, where $$\displaystyle x > y, x\neq 4$$ and 
$$\displaystyle y\neq 1$$ then x + y =


A
7
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B
4
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C
8
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D
10
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Solution

The correct option is D $$10$$
$$ 64 $$ can be written as $$ {64}^{1}, {8}^{2}, {4}^{3}, {2}^{6} $$
As $$ x > y $$
Possible options of writing $$ 64 $$ are $$ {64}^{1}, {8}^{2}, {4}^{3} $$
Since, $$ x \neq 4 $$,
From the chosen options, Possible options of writing $$ 64 $$ are $$ {64}^{1}, {8}^{2} $$
Since, $$ y \neq 1 $$,
From the chosen options, Possible options of writing $$ 64 $$ is only  $$ {8}^{2} $$
So, $$ x = 8, y = 2 $$
$$ => x + y = 10 $$

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