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If 2^(2w) = 8^(w−5), what is the value of w?

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Bunuel
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If 2^(2w) = 8^(w−5), what is the value of w? [#permalink] New post   18 Oct 2019, 03:01
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If \(2^{(2w)} = 8^{(w−5)}\), what is the value of w?

A. 2
B. 3
C. 6
D. 15
E. 18
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D
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If 2^(2w) = 8^(w−5), what is the value of w? [#permalink] New post   18 Oct 2019, 04:55
Bunuel wrote:
If \(2^{(2w)} = 8^{(w−5)}\), what is the value of w?

A. 2
B. 3
C. 6
D. 15
E. 18


\(2^{2w} = 2^{3(w - 5)}\)
2w = 3(w-5) = 3w - 15
w = 15

IMO D
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If 2^(2w) = 8^(w−5), what is the value of w? [#permalink] New post   18 Oct 2019, 05:03
Bunuel wrote:
If \(2^{(2w)} = 8^{(w−5)}\), what is the value of w?

A. 2
B. 3
C. 6
D. 15
E. 18


\(2^{(2w)} = 8^{(w−5)}\)

\(2^{(2w)} = 2^3{(w−5)}\)

\(2w = 3w - 15\)

\(-w = -15\)

\(w = 15\)
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Re: If 2^(2w) = 8^(w−5), what is the value of w? [#permalink] New post   20 Oct 2019, 10:23
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Bunuel wrote:
If \(2^{(2w)} = 8^{(w−5)}\), what is the value of w?

A. 2
B. 3
C. 6
D. 15
E. 18


Noting that 8 = 2^3, we can re-express the right side of the equation:

2^(2w) = (2^3)^(w - 5)

2^(2w) = 2^(3w - 15)

When bases are equal, we can equate the exponents:

2w = 3w - 15

15 = w

Answer: D
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Re: If 2^(2w) = 8^(w−5), what is the value of w? [#permalink] New post   22 Oct 2019, 22:16
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Solution


Given:
    • \(2^{2w} = 8^{w - 5}\)

To find:
    • The value of w

Approach and Working Out:
    • \(2^{2w} = 8^{w - 5}\)
      o Implies, \(2^{2w} = 2^3{w - 5} = 2^{3w – 15}\)

    • Thus, 2w = 3w – 15 (comparing exponents on both sides as the bases are same)

Therefore, w = 15

Hence, the correct answer is Option D.

Answer: D
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Re: If 2^(2w) = 8^(w−5), what is the value of w? [#permalink]
22 Oct 2019, 22:16
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