Solve $2^x+2^{x+1}=1$

Question

I need to solve $$2^x+2^{x+1}=1$$

I have set $y=2^x$ so I get $$y+2y=1$$ $$3y=1$$ $$y=\frac{1}{3}$$ $$2^x=\frac{1}{3}$$

Now I used the $\log$ to get the $x$.

Now I get:

$$x = \log_2{\frac{1}{3}}$$

But the result is wrong, as Wolfram Alpha shows:

$$x=-\frac{\log{3}}{\log{2}}$$

How should I get the $x$?

Answer 1

$\log_2\left(\dfrac13\right) = \log_2\left(3^{-1}\right) = -\log_23 = -\dfrac{\log 3}{\log 2}$