Prove that 2^x+2^(x+1)=3 • 2^x

Question

Prove that 2²+2^x+1=3•2^x

Answer 1

2^x + 2^x+1 = 3 x 2^x

let's remember adding exponents. 2³ x 2² = 2^{3 +2}

So, 2^x+1 = 2^x x 2¹.

Now rewrite this equation as

2^x + (2^x)(2¹) = 3 x 2^x

Let's add a 1 as a multiplier just for clarification.

1 x 2^x + 2 x 2^x = 3 x 2^x

Factor out a 2^x

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

Add the 1 & 2

2^x (3) = 3 x 2^x

or - rewritten

3 x 2^x = 3 x 2^x

Answer 2

2^x+1 = 2^x2¹ = 2(2^x)

So, 2^x + 2^x+1 = 2^x + 2(2^x) = 2^x(1 + 2) = 3(2^x)

Answer 3

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

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

1 + 2^x = 3

2^x = 2

x = 1

True only for x = 1

2²+2^x+1=3•2^x

False, try x = 1