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If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is

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Bunuel
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If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is [#permalink] If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is   31 May 2018, 06:07
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If \(\frac{1}{2^m} + \frac{1}{2^m} = \frac{1}{2^x}\), then x expressed in terms of m is


A. \(\frac{m}{2}\)

B. \(m - 1\)

C. \(m + 1\)

D. \(2m\)

E. \(m^2\)
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B
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Re: If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is [#permalink] If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is   31 May 2018, 06:17
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Solution



Given:
• \(\frac{1}{2^m}\) + \(\frac{1}{2^m}\) = \(\frac{1}{2^x}\)

To find:
• The value of x in terms of m

Approach and Working:
From the given equation, we can write,
    • \(\frac{1}{2^m}\) + \(\frac{1}{2^m}\) = \(\frac{1}{2^x}\)
    Or, \(\frac{2}{2^m}\) = \(\frac{1}{2^x}\)
    Or, \(\frac{2^m}{2}\) = \(2^x\)
    Or, \(2^{m-1}\) = \(2^x\)
    Or, m – 1 = x
    Or, x = m – 1


Hence, the correct answer is option B.

Answer: B
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Re: If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is [#permalink] If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is   31 May 2018, 06:17
\(\frac{1}{2^m} + \frac{1}{2^m} = \frac{1}{2^x}\),

\(\frac{2}{2^m} = \frac{1}{2^x}\)

\(2^{(1 - m)} = 2^{(-x)}\)

Bases equal. Equate the indices.
1 - m = -x
or x = m - 1

Choice B.
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If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is [#permalink] If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is   31 May 2018, 06:18
\(\frac{1}{2^m} + \frac{1}{2^m} = \frac{1}{2^x}\)

\(\frac{2}{2^m} = \frac{1}{2^x}\)

Multiplying \(2^m\) throughout, we get

\(2^1 = 2^{(m-x)}\)

As bases are equal

\(m - x = 1\)

\(x = m - 1\)

Answer B
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Re: If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is [#permalink] If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is   31 May 2018, 06:20
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Bunuel wrote:
If \(\frac{1}{2^m} + \frac{1}{2^m} = \frac{1}{2^x}\), then x expressed in terms of m is


A. \(\frac{m}{2}\)

B. \(m - 1\)

C. \(m + 1\)

D. \(2m\)

E. \(m^2\)


\(\frac{1}{2^m} = 2^{-m}\)

So, \(\frac{1}{2^m} + \frac{1}{2^m} = 2^{-m} + 2^{-m}\)

\(= 2(2^{-m})\)

\(= (2^1)(2^{-m})\)

\(= 2^{1 - m}\)

We can also say that \(\frac{1}{2^x} = 2^{-x}\)

This means we can say: \(2^{1 - m} = 2^{-x}\)

So: 1 - m = -x

Multiply both sides by -1 to get: -1 + m = x

In other words, m - 1 = x

Answer: B
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If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is [#permalink] If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is   31 May 2018, 06:21
Bunuel wrote:
If \(\frac{1}{2^m} + \frac{1}{2^m} = \frac{1}{2^x}\), then x expressed in terms of m is


A. \(\frac{m}{2}\)

B. \(m - 1\)

C. \(m + 1\)

D. \(2m\)

E. \(m^2\)



This one is pretty straight forward question.

(1+1)/\(2^m\) =1 /\(2^x\)
2.\(2^x\) = \(2^m\)
\(2^{x+1}\) =\(2^m\)
x+1 = m
x = m-1

thus , B is the best option.
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Re: If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is [#permalink] If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is   01 Jun 2018, 11:20
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Bunuel wrote:
If \(\frac{1}{2^m} + \frac{1}{2^m} = \frac{1}{2^x}\), then x expressed in terms of m is


A. \(\frac{m}{2}\)

B. \(m - 1\)

C. \(m + 1\)

D. \(2m\)

E. \(m^2\)


Combining the fractions on the left hand side, we have:

2/2^m = 1/2^x

Cross-multiplying yields:

(2)(2^x) = 2^m

Re-expressing 2 as 2^1, we can then simplify the left side:

(2^1)(2^x) = 2^m

2^(1+x) = 2^m

1 + x = m

x = m - 1

Answer: B
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Re: If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is [#permalink] If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is   03 Jun 2018, 02:25
EgmatQuantExpert wrote:

Solution



Given:
• \(\frac{1}{2^m}\) + \(\frac{1}{2^m}\) = \(\frac{1}{2^x}\)

To find:
• The value of x in terms of m

Approach and Working:
From the given equation, we can write,
    • \(\frac{1}{2^m}\) + \(\frac{1}{2^m}\) = \(\frac{1}{2^x}\)
    Or, \(\frac{2}{2^m}\) = \(\frac{1}{2^x}\)
    Or, \(\frac{2^m}{2}\) = \(2^x\)
    Or, \(2^{m-1}\) = \(2^x\)
    Or, m – 1 = x
    Or, x = m – 1


Hence, the correct answer is option B.

Answer: B


hello EgmatQuantExpert

how from this \(\frac{2}{2^m}\) = \(\frac{1}{2^x}\)

you got this \(\frac{2^m}{2}\) = \(2^x\)


pls explain :-)

thank you :)
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If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is [#permalink] If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is   03 Jun 2018, 02:37
GMATPrepNow wrote:
Bunuel wrote:
If \(\frac{1}{2^m} + \frac{1}{2^m} = \frac{1}{2^x}\), then x expressed in terms of m is


A. \(\frac{m}{2}\)

B. \(m - 1\)

C. \(m + 1\)

D. \(2m\)

E. \(m^2\)


\(\frac{1}{2^m} = 2^{-m}\)

So, \(\frac{1}{2^m} + \frac{1}{2^m} = 2^{-m} + 2^{-m}\)

\(= 2(2^{-m})\)

\(= (2^1)(2^{-m})\)

\(= 2^{1 - m}\)

We can also say that \(\frac{1}{2^x} = 2^{-x}\)

This means we can say: \(2^{1 - m} = 2^{-x}\)

So: 1 - m = -x

Multiply both sides by -1 to get: -1 + m = x

In other words, m - 1 = x

Answer: B


hey pushpitkc,

how/why after this \(2^{-m} + 2^{-m}\) we get \(= 2(2^{-m})\) ? :?

shouldnt we get \(4^{-m}\) ?? we need to add bases and not multiply :?

happy sunday :)
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If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is [#permalink] If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is   03 Jun 2018, 03:28
Hi dave13

Write this down somewhere and memorize it - \(a^m*a^n = a^{m+n}\)

(One of the basic rules of exponents)

So, \(2(2^{-m}) = 2^1*2^{-m} = 2^{1-m}\)

Hope this helps you!

Posted from my mobile device
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Re: If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is [#permalink] If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is   03 Jun 2018, 11:31
pushpitkc wrote:
Hi dave13

Write this down somewhere and memorize it - \(a^m*a^n = a^{m+n}\)

(One of the basic rules of exponents)

So, \(2(2^{-m}) = 2^1*2^{-m} = 2^{1-m}\)

Hope this helps you!

Posted from my mobile device



pushpitkc many thanks for explanation ,

but here we are adding bases \(2^{-m} + 2^{-m}\) whereas we apply this formula when we multiply bases \(a^m*a^n = a^{m+n}\) :?
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Re: If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is [#permalink] If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is   03 Jun 2018, 11:39
Expert Reply
dave13 wrote:
pushpitkc wrote:
Hi dave13

Write this down somewhere and memorize it - \(a^m*a^n = a^{m+n}\)

(One of the basic rules of exponents)

So, \(2(2^{-m}) = 2^1*2^{-m} = 2^{1-m}\)

Hope this helps you!

Posted from my mobile device



pushpitkc many thanks for explanation ,

but here we are adding bases \(2^{-m} + 2^{-m}\) whereas we apply this formula when we multiply bases \(a^m*a^n = a^{m+n}\) :?


You are over-complicating this.

\(2^{-m} + 2^{-m}=2*2^{-m}\) the same way x + x = 2x. Substitute x with 2^(-m) and you'll \(2*2^{-m}\). It's that simple.
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Re: If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is [#permalink] If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is   03 Jun 2018, 12:07
Bunuel wrote:
If \(\frac{1}{2^m} + \frac{1}{2^m} = \frac{1}{2^x}\), then x expressed in terms of m is


A. \(\frac{m}{2}\)

B. \(m - 1\)

C. \(m + 1\)

D. \(2m\)

E. \(m^2\)


Given LHS, \(\frac{1}{2^m}\) + \(\frac{1}{2^m}\) =\(2^(-m)\)+\(2^(-m)\)=\(2*2^(-m)\)=\(2^(1-m)\)----------------(1)
Given RHS, \(\frac{1}{2^x}\)=\(2^(-x)\)----------------------------------------------------- (2)

Given LHS=RHS

So \(2^(1-m)\)=\(2^(-x)\)
Implies 1-m=-x

Hence x=m-1.

Ans Option B is the Correct answer.
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Re: If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is [#permalink] If 1/2^m + 1/2^m = 1/2^x, then x expressed in terms of m is   31 Jul 2022, 21:18
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