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What is the value of x^2 – 1 when 9^(x + 1) = 27^(x – 1) ? [#permalink]
Hello!

What's wrong with solving it like the following?

\(x^2 - 1\) = (x+1)(x-1)

(x+1) = 2x +2
(x-1) = 3x - 3

Why it does not reach the same answer?

\(x^2 - 1\) = (2x +2) (3x - 3)

Shouldn't be the same?

Kind regards!
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Re: What is the value of x^2 – 1 when 9^(x + 1) = 27^(x – 1) ? [#permalink]
No it does not. You are mixing two things up. One is the equation given by the question stem. On solving that, as you can see in my solution above, you can come to the conclusion that x = 5.

Second is what the question is asking, it does not ask us the value of x but instead, it asks x^2 - 1.

Equating x^2 - 1 to a product of (2x + 2) and (3x - 3) is bizarre and there is no logical reason why one should do that. That is why I am assuming you mixed things up.

Hope it helps.
jfranciscocuencag wrote:
Hello!

What's wrong with solving it like the following?

\(x^2 - 1\) = (x+1)(x-1)

(x+1) = 2x +2
(x-1) = 3x - 3

Why it does not reach the same answer?

\(x^2 - 1\) = (2x +2) (3x - 3)

Shouldn't be the same?

Kind regards!
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Re: What is the value of x^2 – 1 when 9^(x + 1) = 27^(x – 1) ? [#permalink]
Gladiator59 wrote:
No it does not. You are mixing two things up. One is the equation given by the question stem. On solving that, as you can see in my solution above, you can come to the conclusion that x = 5.

Second is what the question is asking, it does not ask us the value of x but instead, it asks x^2 - 1.

Equating x^2 - 1 to a product of (2x + 2) and (3x - 3) is bizarre and there is no logical reason why one should do that. That is why I am assuming you mixed things up.

Hope it helps.
jfranciscocuencag wrote:
Hello!

What's wrong with solving it like the following?

\(x^2 - 1\) = (x+1)(x-1)

(x+1) = 2x +2
(x-1) = 3x - 3

Why it does not reach the same answer?

\(x^2 - 1\) = (2x +2) (3x - 3)

Shouldn't be the same?

Kind regards!


Thank you very much Gladiator59 !

Yes, now that I read it again it doe not make more sense to me, I guess I was tired.

Kind regards!
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Re: What is the value of x^2 – 1 when 9^(x + 1) = 27^(x – 1) ? [#permalink]
Expert Reply
Bunuel wrote:
What is the value of \(x^2 - 1\) when \(9^{x+ 1} = 27^{x - 1}\) ?

A. 8
B. 12
C. 18
D. 24
E. 32


In order to solve for x, we need a common base for each expression in the equation. Note that 9 = 3^2 and 27 = 3^3. Simplifying, we have:

3^(2x + 2) = 3^(3x - 3)

2x + 2 = 3x - 3

5 = x

So x^2 - 1 = 24.

Answer: D
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Re: What is the value of x^2 – 1 when 9^(x + 1) = 27^(x – 1) ? [#permalink]
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