There is this example in my book of solving an exponential equation using factor

Question

There is this example in my book of solving an exponential equation using factoring, but I don't understand one part of it.

2^(x+2) - 2^x = 96
2^2 x 2^x - 2^x = 96
4 x 2^x - 2^x = 96
(4-1)2^x = 96     <--- factor out 2^x
3 x 2^x = 96
2^x = 32
2^x = 2^5
x=5 It is the parts highlighted in yellow that I do not understand. I don't understand how we go from 4 x 2^x - 2^x to (4-1)2^x . Can anyone help me? I will rate well! Thank you. There is this example in my book of solving an exponential equation using factoring, but I don't understand one part of it.

2^(x+2) - 2^x = 96
2^2 x 2^x - 2^x = 96
4 x 2^x - 2^x = 96
(4-1)2^x = 96     <--- factor out 2^x
3 x 2^x = 96
2^x = 32
2^x = 2^5
x=5 It is the parts highlighted in yellow that I do not understand. I don't understand how we go from 4 x 2^x - 2^x to (4-1)2^x . Can anyone help me? I will rate well! Thank you.

Explanation / Answer

You can look at 4* 2^x- 2^x as 4*2^x- 1*2^x So if we factor out the 2^x we get 2^x (4-1)= 3*2^x.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.