Algebra Question, How can I prove, 2^x + 2^(x+1) = 3*2^x ?

Question

All I can think of is to say is, make x any number and prove the equation, but I don't think that's the correct answer.

Answer 1

The trick is to first separate the second term 2^(x+1) into it's product which = (2^x)(2^1).

{You can do this because when you multiply exponents with the same base, in this case 2, then you just keep your base and add the exponents.}

Then rewrite your original equation in [(2^x)+ (2^x)*(2^1)] Right? The second step is to FACTOR OUT 2^x from the first and second term which gives you:

[(2^x)+ (2^x)*(2^1)] = 2^x [ 1+2^1 ].

{You can see this is true if you just distribute back the 2^x into it to get the original equation}

The Final step is to remember that any number raised to the power of ONE is equal to itself, then
2^1 = 2, then . So, 2^x (2+1) = 2^x(3) or in reverse order 3(2^x).

Answer 2

You'll have to work with some bad spacing, because yahoo won't allow the spacing to put the number under the lines in the right place. Sorry.

2^x + 2^(x+1) = 3*2^x

Divide both sides by 3*2^x

2^x + 2^(x+1) = 3*2^x
--------------------------------
3*2^x

You then break up the left side into.

2^x 2^(x+1)
------ + ----------- = 1
3*2^x 3*2^x

The 2^x cancel in the first term and the second term you can pull out the 1/3

1 1 2^(x+1)
-- + -- --------- = 1
3 3 2^x

The top of the second term can be broken into these two parts.

1 1 (2^x) X (2^1)
-- + -- --------------- = 1
3 3 2^x

The 2^x cancel in the second term.

1 1 1 X 2^1
-- + -- ------------- = 1
3 3 1

From this point it’s simple multiplication and addition.

1 2
-- + -- = 1
3 3

1=1

Answer 3

Have you learned to prove by induction yet?

I am short on time, so I can't actually try it out, but with the use of x and x+1, it looks possible.

Give that a shot, and I hope to come back in time to try it out...unless someone else solves it.

Edit: Ha, don't I feel silly. You just need to factor it.

First, factor out 2^x:
2^x + 2^(x+1) = 2^x(1+2^1) = 2^x(1+2) = 3* 2^x

I was worried over nothing.

Edit: Akilesh, that is twice now I saw you "prove" something by solving for one value of x. If you cannot provide a proof, please do not confuse the issue.

Answer 4

2^x + 2^(x+1) = 3*2^x
Take x = 2
2^2 + 2^(2+1) = 3*2^2
4 + 2^3 = 3*4
4 + 8 = 12
12 = 12
LHS = RHS
The equation is proved true

Answer 5

2^x + 2^(x+1) = 3*2^x
1+2=3(dividing above equation by 2^x)
3=3

(2^x + 2^(x+1)
=2^x(1+2^1)
=2^x(1+2)
=2^x*3)

Answer 6

Apply the laws of arithmetic operations.
What does 2^(x+1) mean? 2^3 = 2*2*2; 2^4 = 2*2*2*2
So 2^(x+1) = 2^x * 2.

Now you have 2^x + 2^x * 2. Does that answer you?

Answer 7

2^x + 2^(x+1) = 3*2^x

2^x + (2^x)2^1 = 3*2^x
divive all terms by 2^x

2^x/2^x + (2^x)2^1/2^x = 3*2^x/2^x
1 + 2^1 = 3
1 + 2 = 3
3 = 3

Answer 8

this is very eazy.do you know this rule.

2^(x+1) =2*2^(x)
then we just have to put this in to the left hand side of this equation.
L.H.S=2^(x)+2^(x+1)

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

=3*2^(x)
so you dosen't have to submit any numbers.
i think my answer is a good one.

Answer 9

2^x + 2^(x+1) = 3*2^x

LHS:
2^x + 2^(x+1)
= 2^x + 2^x * 2

Let 2^x be y, therefore:

y + 2y = 3y
3y = 3 * 2^x (proven)