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# If 2^199 + 2^199 = 2^x, what is the value of x?

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If 2^199 + 2^199 = 2^x, what is the value of x?  [#permalink]

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31 Jul 2019, 02:02
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If $$2^{199} + 2^{199} = 2^x$$, what is the value of x?

A. 199
B. 200
C. 201
D. 202
E. 203

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Posts: 717
If 2^199 + 2^199 = 2^x, what is the value of x?  [#permalink]

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Updated on: 31 Jul 2019, 02:11
$$2^{199}$$+$$2^{199}$$=$$2^x$$
$$2*2^{199}$$=$$2^{200}$$=$$2^x$$
--> x=200

Originally posted by lacktutor on 31 Jul 2019, 02:06.
Last edited by lacktutor on 31 Jul 2019, 02:11, edited 2 times in total.
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If 2^199 + 2^199 = 2^x, what is the value of x?  [#permalink]

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31 Jul 2019, 02:09
Bunuel wrote:
If $$2^{199} + 2^{199} = 2^x$$, what is the value of x?

A. 199
B. 200
C. 201
D. 202
E. 203

$$2^{199} + 2^{199} = 2^x$$
$$2*2^{199} = 2^{200} = 2^x$$
x= 200

IMO B
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Re: If 2^199 + 2^199 = 2^x, what is the value of x?  [#permalink]

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31 Jul 2019, 02:18
We have to take common as we can't do anything to exponents separated via addition sign

Therefore,
2^199(1+1) = 2^199*2

Now we can add them, as 2= 2^1

So, 2^(199+1)
2^200=2^x
X= 200 (B)

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Re: If 2^199 + 2^199 = 2^x, what is the value of x?  [#permalink]

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01 Aug 2019, 12:42
2^199+2^199=2^x
Let y=2^199
y+y=2^x
2y=2^x
2*2^199=2^x
2^200=2^x
Therefore x=200
Hence B.

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Re: If 2^199 + 2^199 = 2^x, what is the value of x?  [#permalink]

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06 Aug 2019, 16:39
Bunuel wrote:
If $$2^{199} + 2^{199} = 2^x$$, what is the value of x?

A. 199
B. 200
C. 201
D. 202
E. 203

2^199 is a common factor of both terms on the left side of the equation. Simplifying, we have:

2^199(1 + 1) = 2^x

2^199 * 2^1 = 2^x

2^200 = 2^x

200 = x

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Re: If 2^199 + 2^199 = 2^x, what is the value of x?   [#permalink] 06 Aug 2019, 16:39