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

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Bunuel
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2^x + 2^(x+3)=6^2*2^18. What is the value of x? [#permalink] 2^x + 2^(x+3)=6^2*2^18. What is the value of x?   01 Mar 2017, 01:58
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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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B
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2^x + 2^(x+3)=6^2*2^18. What is the value of x? [#permalink] 2^x + 2^(x+3)=6^2*2^18. What is the value of x?   01 Mar 2017, 02:27
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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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Re: 2^x + 2^(x+3)=6^2*2^18. What is the value of x? [#permalink] 2^x + 2^(x+3)=6^2*2^18. What is the value of x?   02 Oct 2018, 10:11
Hello , Bunuel
2^x *9 = 9^2 *2^20
how can we remove 9 and 9^2 together here ?
could u explain please?
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Re: 2^x + 2^(x+3)=6^2*2^18. What is the value of x? [#permalink] 2^x + 2^(x+3)=6^2*2^18. What is the value of x?   02 Oct 2018, 21:10
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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



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

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

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

\(2^x = 2^{20}\);

\(x=20\).

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

Answer: B
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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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