Powinniśmy zauważyć, że:
$$(\sqrt{2})^2=(2^\frac{1}{2})^2=2^{\frac{1}{2}\cdot2}=2^1 \           ,\
(\sqrt{2})^4=(2^\frac{1}{2})^4=2^{\frac{1}{2}\cdot4}=2^2=4 \           ,\
(\sqrt{2})^8=(2^\frac{1}{2})^8=2^{\frac{1}{2}\cdot8}=2^4=16$$

Skoro tak, to podstawiając te dane do naszego logarytmu, otrzymamy:
$$log_{2}\left[(\sqrt{2})^2\cdot(\sqrt{2})^4\cdot(\sqrt{2})^8\right]= \           ,\
=log_{2}(2^1\cdot2^2\cdot2^4)= \           ,\
=log_{2}(2^{1+2+4})=log_{2}2^7=7$$