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If x is a positive integer, and m=1^(x+1), then what is the value of

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If x is a positive integer, and m=1^(x+1), then what is the value of  [#permalink]

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New post 06 Oct 2018, 10:10
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  45% (medium)

Question Stats:

68% (01:56) correct 32% (02:24) wrong based on 130 sessions

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If x is a positive integer, and \(m=3^{x+1}\), then what is the value of \(9^{2x}\) in terms of m?

a) \(\frac{m^2}{9}\)

b) \(\frac{m^2}{81}\)

c) \(\frac{m^3}{9}\)

b) \(\frac{m^4}{3}\)

e) \(\frac{m^4}{81}\)
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Re: If x is a positive integer, and m=1^(x+1), then what is the value of  [#permalink]

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New post 06 Oct 2018, 11:41
1
m=3^(x+1)

=> m=3^x* 3

=> m/3 = 3^x

Also, 9^2x = 9^x *9^x => (3^x)^2 * (3^x)^2

=> (m/3)^2*(m/3)^2 => m^4/81

Hence Ans: E
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Re: If x is a positive integer, and m=1^(x+1), then what is the value of  [#permalink]

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New post 06 Oct 2018, 12:20
Put \(x=1\) in \(m\)=\(3^{x+1}\) ==>\(m=3^2\) ==> \(9\)

Now ,Put \(x=1\) in \(9^{2x}\) ==> \(81\)

Now put \(m=9\) in answer options to get \(81\)

Only option E gives \(81\)


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Re: If x is a positive integer, and m=1^(x+1), then what is the value of  [#permalink]

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New post 18 Jan 2019, 20:52
Hello!

Could someone please provide an algebraic solution?

Kind regards!
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Re: If x is a positive integer, and m=1^(x+1), then what is the value of  [#permalink]

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New post 18 Jan 2019, 21:04
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jfranciscocuencag wrote:
Hello!

Could someone please provide an algebraic solution?

Kind regards!


m=3^(x+1)

Can be written as => m = \(3^x\) * 3 -----(a)

To find \(9^{2x}\) in terms of m

lets expand the question a bit, \(3^{4x}\)

\(3^x * 3^x * 3^x * 3^x\)

Now you can manipulate (a) as \(3^x\) = m / 3

Just substitute that back into the question, to get m^4 / 81

Does this help in any way ??
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If x is a positive integer, and m=1^(x+1), then what is the value of  [#permalink]

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New post 19 Jan 2019, 12:32
1
KanishkM wrote:
jfranciscocuencag wrote:
Hello!

Could someone please provide an algebraic solution?

Kind regards!


m=3^(x+1)

Can be written as => m = \(3^x\) * 3 -----(a)

To find \(9^{2x}\) in terms of m

lets expand the question a bit, \(3^{4x}\)

\(3^x * 3^x * 3^x * 3^x\)

Now you can manipulate (a) as \(3^x\) = m / 3

Just substitute that back into the question, to get m^4 / 81

Does this help in any way ??


Hello KanishkM !

Well no, it does not.

I¿m having problems to get to the answer from the easiest way.

Could you please explain to me how to solve it by plugging values, I have spent 2 hours but still don't know how to get the answer.

Thank you very much for your reply!
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If x is a positive integer, and m=1^(x+1), then what is the value of   [#permalink] 19 Jan 2019, 12:32
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