I don't understand how you can get -2 out of log base 2 1/4 ?
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$\displaystyle \log_2 \frac{1}{4} = \log_2 \frac{1}{2^2} = \log_2 2^{-2}= -2 \times \log_2 2 = -2 \times 1$
Logarithmic identities
Here's another way: $\displaystyle \log_2 \frac{1}{4}=x$ is equivalent to $\displaystyle 2^x=\frac{1}{4}=2^{-2}$. So $\displaystyle x=-2$.
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