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timofeeve [1]
3 years ago
6

If 2^(x+3) - 2x = k(2^x) what is the value of k

Mathematics
1 answer:
svlad2 [7]3 years ago
8 0

Answer:

\large\boxed{C)\ 7}

Step-by-step explanation:

Use:

a^n\cdot a^m=a^{n+m}

2^{x+3}-2^x=2^x\cdot2^3-2^x=8\cdot2^x-2^x=(8-1)\cdot2^x=7\cdot2^x\\\\2^{x+3}-2^x=k(2^x)\\\\7\cdot2^x=k(2^x)\Rightarrow k=7

8\cdot2^x-2^x=8\cdot2^x-1\cdot2^x=(8-1)(2^x)=7\cdot2^x\\\\\text{distributive property:}\ a(b-c)=ab-ac

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