Question

If 4^44 +4^44 + 4^44 + 4^44 = 4^x, then x is
(1) 45
(2) 44
(3) 176
(4) 11
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Answer 1

$4^{44}+4^{44}+4^{44}+4^{44}=4^x$

At LHS,  $4^{44}$  is added 4 times, so we can briefly write it as 4 multiplied by  $4^{44},$  i.e.,

$4 \times 4^{44}=4^x$

4 can be taken as 4¹.

$4^1 \times 4^{44} = 4^x$

Using the identity  $a^m \times a^n = a^{m+n},$  we get,

$4^{1+44}=4^x$

which implies,

$4^{45}=4^x$

Hence.

$\Large \boxed{\ \ \ \mathbf{x = 45}\ \ \ }$

Thus the answer is option (1).

Answer 2

Answer:

option(1) 45 is correct

Step-by-step explanation:

4^44 +4^44 + 4^44 + 4^44 = 4^x

4*4^44=4^x

4^1*4^44=4^x

as base is same so powers will be added

So 4^(1+44)=4^x

Both sides bases are same so powers will be equal

hence 1+44=x

x=45

option(1) is correct