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If 1/2^m +

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If 1/2^m + [#permalink] New post 07 Mar 2018, 15:31
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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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[Reveal] Spoiler: OA

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Re: If 1/2^m + [#permalink] New post 07 Mar 2018, 19:28
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To get rid of all the fractions, multiply all terms by 2^m and by 2^x to get:

2^x +2^x = 2^m

Collect similar terms:

2x2^x = 2^m

Collect same bases on the left by thinking of the 2 as 2^1:

2^1x2^x = 2^m

Multiplying the same bases with different exponents cant be done by adding the exponents:

2^(1+x) = 2^m

Now we can ignore the bases:

1+x = m

Subtract 1:

x = m - 1

The answer is B.
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Re: If 1/2^m +   [#permalink] 07 Mar 2018, 19:28
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