Question

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

A) 3
B) 5
C) 7
D) 8

Please show me how to do this

Answer 1

Answer:

$\large\boxed{C)\ 7}$

Step-by-step explanation:

Use:

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

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

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

Answer 2

Given:

The equation is:

$2^{x+3}-2^x=k(2^x)$

To find:

The value of $k$.

Solution:

We have,

$2^{x+3}-2^x=k(2^x)$

Using the property of exponents, we get

$2^{x}2^{3}-2^x=k(2^x)$          $[\because a^{m+n}=a^ma^n]$

$8(2^{x})-2^x=k(2^x)$

$7(2^x)=k(2^x)$

On comparing both sides, we get

$k=7$

Therefore, the value of $k$ is 7. Hence option C is correct.

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