1. ## 2^(x)2^(x+1)2^(x+2)=2^6

2^(x)2^(x+1)2^(x+2)=2^6

Find all integers for the equation.

2. Originally Posted by techmath
2^(x)2^(x+1)2^(x+2)=2^6

Find all integers for x the equation.
By exponent properties, this is the same as $\displaystyle 2^{x+x+1+x+2}=2^6\implies 2^{3x+3}=2^6$. This now implies that $\displaystyle 3x+3=6$.

Can you continue?

3. Originally Posted by Chris L T521
By exponent properties, this is the same as $\displaystyle 2^{x+x+1+x+2}=2^6\implies 2^{3x+3}=2^6$. This now implies that $\displaystyle 3x+3=6$.

Can you continue?
I am extremly sorry!

it is supposed to be: 2^(x)+2^(x+1)+2^(x+2)=2^6

4. Originally Posted by techmath
I am extremly sorry!

it is supposed to be: 2^(x)+2^(x+1)+2^(x+2)=2^6
Factor by $\displaystyle 2^x$ :
$\displaystyle 2^x(1+2+4)=2^6$

$\displaystyle 7 \cdot 2^x=2^6$

7 divides the left hand side. Thus it has to divide the right hand side, which is not possible !

So there is no positive solution to this equation.