Because: Log (1/16) / Log (2) =-4, You may try it on a calculator, so that:
2^-4 =1/16.
+118629 log2(1/16) = -4
It is a bit complex for a 12 year old. :) But a log is a power,
\(If\;\;log_2\frac{1}{16}= -4\;\;\;then\\ 2^{-4} \;\;must \;\;equal\;\; \frac{1}{16}\\~\\ \frac{2^{-4}}{1}=\frac{1}{2^{+4}}\qquad \mbox{because that is how negative indices work}\\ \frac{1}{2^4}=\frac{1}{2*2*2*2}=\frac{1}{16}\\ so\\log_2\frac{1}{16}= -4 \)
