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# 2^x + 2^(x+3)=6^2*2^18. What is the value of x?

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Math Expert
Joined: 02 Sep 2009
Posts: 55150
2^x + 2^(x+3)=6^2*2^18. What is the value of x?  [#permalink]

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01 Mar 2017, 01:58
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Difficulty:

5% (low)

Question Stats:

88% (01:22) correct 12% (02:29) wrong based on 104 sessions

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$$2^x + 2^{(x+3)}=6^2*2^{18}$$. What is the value of x?

A. 18
B. 20
C. 21
D. 22
E. 24

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2^x + 2^(x+3)=6^2*2^18. What is the value of x?  [#permalink]

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01 Mar 2017, 02:27
1
Bunuel wrote:
$$2^x + 2^{(x+3)}=6^2*2^{18}$$. What is the value of x?

A. 18
B. 20
C. 21
D. 22
E. 24

$$2^x + 2^{(x+3)} = 6^2*2^{18}$$
$$2^x*(1 + 2^3) = (3*2)^2*2^{18}$$
$$2^x*(9) = (9)^2*2^{20}$$
$$2^x = 2^{20}$$

x=20

Hence option B is correct
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Joined: 08 Feb 2018
Posts: 5
Re: 2^x + 2^(x+3)=6^2*2^18. What is the value of x?  [#permalink]

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02 Oct 2018, 10:11
Hello , Bunuel
2^x *9 = 9^2 *2^20
how can we remove 9 and 9^2 together here ?
Math Expert
Joined: 02 Sep 2009
Posts: 55150
Re: 2^x + 2^(x+3)=6^2*2^18. What is the value of x?  [#permalink]

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02 Oct 2018, 21:10
1
Bunuel wrote:
$$2^x + 2^{(x+3)}=6^2*2^{18}$$. What is the value of x?

A. 18
B. 20
C. 21
D. 22
E. 24

$$2^x + 2^{(x+3)}=6^2*2^{18}$$;

$$2^x*(1 + 2^3) = (3*2)^2*2^{18}$$;

$$2^x*(9) = 9*2^2*2^{18}$$;

$$2^x = 2^{20}$$;

$$x=20$$.

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Re: 2^x + 2^(x+3)=6^2*2^18. What is the value of x?  [#permalink]

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03 Oct 2018, 17:53
Bunuel wrote:
$$2^x + 2^{(x+3)}=6^2*2^{18}$$. What is the value of x?

A. 18
B. 20
C. 21
D. 22
E. 24

Simplifying, we have:

2^x + (2^x)(2^3) = 6^2 * 2^18

Factoring out the common 2^x from both terms on the left side of the equation, we have:

(2^x)(1 + 2^3) = 36 * 2^18

(2^x)(9) = 36 * 2^18

2^x = 4 * 2^18

2^x = 2^20

x = 20

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Re: 2^x + 2^(x+3)=6^2*2^18. What is the value of x?   [#permalink] 03 Oct 2018, 17:53
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