Question

If 2x+3 – 2^x = k(2^x), what is the value of k?

Answer 1

The equation given is:

`2^(x+3)-2^x=k(2^x)`

We can use the property:

`a^(b+c)=a^ba^c`

to break this apart. Shown below:

`\begin{gathered} 2^(x+3)-2^x=k(2^x) \\ 2^x2^3-2^x=k(2^x) \end{gathered}`

We can solve for k [we divide both sides by 2^x to isolate k]:

`\begin{gathered} 2^x2^3-2^x=k(2^x) \\ k=(2^x2^3-2^x)/(2^x) \end{gathered}`

Now, let's do a little algebra. The steps are shown below:

`\begin{gathered} k=(2^x2^3-2^x)/(2^x) \\ k=(2^x2^3)/(2^x)-(2^x)/(2^x) \\ k=2^3-1 \\ k=8-1 \\ k=7 \end{gathered}`

The correct answer is

C