math help!!?

Question

If 4^x - 2^(x+1) += 48, find x.

my teacher gave us this homework without further explanation. i can't find in our books how to solve this. please help.

Answer 1

I shall assume you mean 4^x - 2^(x+1) = 48.
Let 2^x be y.
Since 4^x = 2^(2x),
y^2 - (2^x * 2) = 48
y^2 - 2y = 48
y^2 - 2y - 48 = 0
(y-8)(y+6)=0
y=8 or -6
Since 2^x must be positive, we must reject y = -6 .
2^x = 8
We know that the CUBE of 2 is 8.
Hence, 2 to the power of 3 is 8.
In conclusion, x = 3.

Answer 2

4^x - 2^(x+1) = 48

4 can also be expressed as 2*2
Also 2^(x+1) is the same as 2^x * 2^1, or (2 * 2^x)

So the equation becomes

(2*2)^x - (2 * 2^x) = 48

2^x * 2^x - (2^x + 2^x) = 48

Assume 2^x = a

So the above equation becomes:

a^2 - 2a = 48
or

a^2 + 6a - 8a - 48 = 0

a(a+6) - 8(a+6) = 0
(a-8)(a+6) = 0
For the above expression to be true, either (a+6) must be Zero, or (a-8) must be Zero. Because you can ONLY get Zero as a product of 2 numbers if one of these 2 numbers is Zero.

Let's take a+6=0, which means a = -6, which is impossible because 2^x CANNOT be equal to a negative number.

So, that leaves us with a-8=0, which means a = 8.

So 2^x = 8
8 can be expressed as 2^3
So 2^x = 2^3

Therefore x = 3

Answer 3

4^x=2^2x=2^2 *2^x=4 * 2^x
2^(x+1)=2^x *2
let 2^x=a
so 4^x-2^(x+1)=4a-2a=2a
2a=48
a=48/2
a=12
so 2^x=12

Answer 4

Hehehe. This is one that you actually have to think about ☺
Remember the Laws of Exponents:
(x^a)*(x^b) = x^(a+b) and
(x*y)^a = (x^a)*(y^a)
Now look at the problem again and see if you can't find a way to simplify the left-hand side.
(I know...... I'm a rotten bastard. But if I do it, you'll -never- learn to think for yourself ☺)

Doug

Answer 5

the question is really hard...are you sure that the equation is just right?