If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is

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If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink]

10 Jul 2008, 19:05

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If 27^(4x + 2) × 162^-2x × 36^x × 9^(6 – 2x) = 1, then what is the value of x?

A. -9
B. -6
C. 3
D. 6
E. 9

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Re: PS - Powers, what is the value of x? [#permalink]

10 Jul 2008, 19:14

x-ALI-x wrote:

If 27^(4x + 2) × 162^-2x × 36^x × 9^(6 – 2x) = 1, then what is the value of x?

A) -9
B) -6
C) 3
D) 6
E) 9

(3^3)^(4x + 2) * (3^4 * 2)^-2x * (3^2 * 2^2) ^x * (3^2)^(6-2x) = 1

the 2 ^ -2x from second term and 2^2x from the third term gets canclled

giving us all all terms with base 3.

3^ (2x + 18) = 1

2x + 18 must be 0 in order to satisfy this

x= -9

A

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Re: If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink]

14 Nov 2012, 13:03

This is the last part of the answer from the CAT explanation.

2^0 × 3^2x + 18 = 1
3^2x + 18 = 1
3^2x + 18 = 3^0
2x + 18 = 0
2x = -18
x = -9

where does the 3^0 comes from?

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Re: If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink]

14 Nov 2012, 13:06

3^0 is substituted for 1 to show both sides of the equation with the same base

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Re: If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink]

04 Jan 2013, 05:10

Can anyone explain how the 18 comes into play?

Also 2^0 in the second explanation.

Thanks.

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Re: If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink]

04 Jan 2013, 06:08

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xALIx wrote:

If 27^(4x + 2) × 162^-2x × 36^x × 9^(6 – 2x) = 1, then what is the value of x?

A. -9
B. -6
C. 3
D. 6
E. 9

27^{4x + 2} * 162^{-2x} * 36^x * 9^{6-2x} = 1

3^{3*(4x + 2)} * (2^{-2x}*81^{-2x}) * (4^{x}*9^x) * 3^{2(6-2x)} = 1

3^{3*(4x + 2)} * (2^{-2x}*3^{-8x}) * (2^{2x} *3^{2x})* 3^{2(6-2x)} = 1 --> 2^{-2x}*2^{2x}=1. So, we have that:

3^{3*(4x + 2)-8x+2x+2(6-2x)} = 1

3^{2x+18}=1 --> 2x+18=0 --> x=-9.

Answer: A.
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Re: If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink]

16 May 2013, 12:38

Quick question: How I am I supposed to know that 162 equals 2*3^4 ??? Is there a calculation to it or is 81= 3^4 common knowledge? thanks

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Re: If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink]

16 May 2013, 23:58

NicolasFSS wrote:

Quick question: How I am I supposed to know that 162 equals 2*3^4 ??? Is there a calculation to it or is 81= 3^4 common knowledge? thanks

If you don't know that 81=3^4 you can do the following: 162=2*81=2*9*9=2*3^2*3^2=2*3^4.

I'd advice to know the powers of 2 till 2^10 and the powers of 3 till 3^5.
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Re: If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is [#permalink] 16 May 2013, 23:58

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If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is

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If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is

If 27^(4x + 2) 162^-2x 36^x 9^(6 2x) = 1, then what is

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