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If 16^(2x+3) = 8^(x-1), what is the value of x?

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If 16^(2x+3) = 8^(x-1), what is the value of x?  [#permalink]

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New post 13 Jul 2018, 09:02
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If \(16^{2x+3} = 8^{x-1}\) , what is the value of x?

1. -3
2. -1
3. 0
4. 1
5. 3

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Re: If 16^(2x+3) = 8^(x-1), what is the value of x?  [#permalink]

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New post 13 Jul 2018, 09:14
\(16^{2x+3} = 8^{x-1}\)

=> \(2^{4(2x+3)} = 2^{3(x-1)}\)

Since the bases are equal, the exponents must be equal

=> \(4(2x + 3) = 3(x-1)\)

=> \(8x + 12 = 3x - 3\)

=> \(5x = -15\)

=> \(x = -3\)

Hence option A
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Re: If 16^(2x+3) = 8^(x-1), what is the value of x?  [#permalink]

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New post 13 Jul 2018, 09:17
AkshdeepS wrote:
If \(16^{2x+3} = 8^{x-1}\) , what is the value of x?

1. -3
2. -1
3. 0
4. 1
5. 3



\(16^{2x+3} = 8^{x-1}\)
or, \(2^{4(2x+3)} = 2^{3(x-1)}\)

Hence , \(4(2x+3) = 3(x-1)\)
or, \(8x+12 = 3x-3\)
or, \(5x = -15\)
or, \(x = -3\)...................Hence I would go for option A.
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Re: If 16^(2x+3) = 8^(x-1), what is the value of x? &nbs [#permalink] 13 Jul 2018, 09:17
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