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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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13 Jul 2018, 10:02
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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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13 Jul 2018, 10:14
$$16^{2x+3} = 8^{x-1}$$

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

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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13 Jul 2018, 10:17
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?   [#permalink] 13 Jul 2018, 10:17
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