If $4^{44} + 4^{44} + 4^{44} + 4^{44} = 4^{x}$ , then $x$ is ___.

45

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44

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176

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11

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Solution

The correct option is C $45$
By Solving L.H.S we get,
$= 4^{44} + 4^{44} + 4^{44} + 4^{44}$
Taking $4^{44}$ we get,
$= 4^{44} (1 + 1 + 1 + 1)$
$= 4^{44} \times 4$
$= 4^{44 + 1}$
$= 4^{45}$
Now, Compairing it with R.H.S,
$⟹ 4^{45} = 4^{x}$
For the same base Exponent must be same.
$∴ x = 45$

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