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# What is the value of x2 – 1 when 9x+ 1 = 27x– 1 ?

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What is the value of x2 – 1 when 9x+ 1 = 27x– 1 ? [#permalink]  15 May 2018, 16:07
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Question Stats:

100% (01:15) correct 0% (00:00) wrong based on 8 sessions
What is the value of $$x^2 - 1$$ when $$9^{x+ 1} = 27^{x - 1}$$ ?

[Reveal] Spoiler: OA
24

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Sandy
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Kudos [?]: 31 [1] , given: 22

Re: What is the value of x2 – 1 when 9x+ 1 = 27x– 1 ? [#permalink]  16 May 2018, 21:11
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At first this problem looks complicated, but let's simplify this a little.

When we see $$9^{x+ 1} = 27^{x - 1}$$, we can change it like so. $$3^2(x+ 1) = 3^3(x - 1)$$.
How? $$3^2 = 9$$ and $$3^3=27$$.

From there, you can focus exclusively on the exponents. $$2(x+1)=3(x-1)$$
$$2x + 2 = 3x - 3$$
$$5 = x$$

Plus in 5 for the original equation.
$$x^2-1=?$$
$$5^2-1=24$$

The value of $$x^2 - 1$$ when $$9^{x+ 1} = 27^{x - 1}$$ is 24.
Re: What is the value of x2 – 1 when 9x+ 1 = 27x– 1 ?   [#permalink] 16 May 2018, 21:11
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