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Find the value of y given that 4^(y^2)/64 = 2^(-y) and y < |y|

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Bunuel
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Find the value of y given that 4^(y^2)/64 = 2^(-y) and y < |y| [#permalink] New post   27 Sep 2021, 07:45
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Find the value of y given that \(\frac{4^{y^2}}{64}=2^{-y}\) and \(y < |y|\)

A. -4
B. -3
C. -2
D. -1
E. 2
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C
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Re: Find the value of y given that 4^(y^2)/64 = 2^(-y) and y < |y| [#permalink] New post   27 Sep 2021, 09:31
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Bunuel wrote:
Find the value of y given that \(\frac{4^{y^2}}{64}=2^{-y}\) and \(y < |y|\)

A. -4
B. -3
C. -2
D. -1
E. 2


\(\frac{2^{2y^2}}{2^6} = 2^{-y}\)
\(2y^2 - 6 = -y\)
\(2y^2 + 4y - 3y - 6 = 0\)
\(2y(y + 2) - 3(y + 2) = 0\)
y = \(\frac{3}{2}\); y = -2
Since, y < |y| y = -2

IMO, (C)!
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Bunuel
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Re: Find the value of y given that 4^(y^2)/64 = 2^(-y) and y < |y| [#permalink] New post   03 Nov 2021, 07:56
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Bunuel wrote:
Find the value of y given that \(\frac{4^{y^2}}{64}=2^{-y}\) and \(y < |y|\)

A. -4
B. -3
C. -2
D. -1
E. 2





This question is a part of Are You Up For the Challenge: 700 Level Questions collection.
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nermeendhuca
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Re: Find the value of y given that 4^(y^2)/64 = 2^(-y) and y < |y| [#permalink] New post   20 Nov 2021, 14:55
I don't get it. If I plug in y=-2 it doesn't work...

y^2/16 = 2^-y

plug in y=-2

4/16 = 4
... 1/4= 4 <-- not equal

What am I doing wrong?
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mintchoco
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Re: Find the value of y given that 4^(y^2)/64 = 2^(-y) and y < |y| [#permalink] New post   20 Nov 2021, 21:42
nermeendhuca wrote:
I don't get it. If I plug in y=-2 it doesn't work...

y^2/16 = 2^-y

plug in y=-2

4/16 = 4
... 1/4= 4 <-- not equal

What am I doing wrong?


I used to have the same thought as you, but giving the equation a second look has enabled me to know what my fault was :)
It's 4 to the power of y to the power of 2 (4^y^2), not 4 times y^2 (4y^2). I had the wrong answer as I see things in the former way.
(C) is the correct answer.
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Re: Find the value of y given that 4^(y^2)/64 = 2^(-y) and y < |y| [#permalink] New post   17 Jul 2023, 17:57
When raising an exponential term to an exponent, you can multiply the exponents but how come in this case, if we do that, we get a different answer? For example, why can't 4^(y^2 ) be simplified to 4^(2y)?
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Find the value of y given that 4^(y^2)/64 = 2^(-y) and y < |y| [#permalink] New post   17 Jul 2023, 22:03
tinamar wrote:
When raising an exponential term to an exponent, you can multiply the exponents but how come in this case, if we do that, we get a different answer? For example, why can't 4^(y^2 ) be simplified to 4^(2y)?



Operations involving the same exponents:
Keep the exponent, multiply or divide the bases
\(a^n*b^n=(ab)^n\)

\(\frac{a^n}{b^n}=(\frac{a}{b})^n\)

\((a^m)^n=a^{mn}\)

\(a^{m^n}=a^{(m^n)}\) and not \((a^m)^n\)


Check the thread: https://gmatclub.com/forum/exponents-an ... 74993.html
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Find the value of y given that 4^(y^2)/64 = 2^(-y) and y < |y| [#permalink]
17 Jul 2023, 22:03
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