Question

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

A
7
B
4
C
8
D
10

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, $$x = 8, y = 2$$$$=> x + y = 10$$Maths

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