[tex]\Large\boxed{\begin{array}{l}\rm d)~\sf(0,2)^{3x}=1\\\sf(0,2)^{3x}=(0,2)^0\\\sf 3x=0\\\sf x=\dfrac{0}{3}\\\\\sf x=0\end{array}}[/tex]

[tex]\Large\boxed{\begin{array}{l}\rm e)~\sf2^{x-4}+2^x+2^{x+2}=44\\\sf\dfrac{2^x}{2^4}+2^x+2^x\cdot2^2=44\\\\\sf\dfrac{2^x}{16}+2^x+2^x\cdot4=44\times(16)\\\\\sf 2^x+16\cdot2^x+64\cdot2^x=704\\\sf81\cdot2^x=704\\\sf 2^x=\dfrac{704}{81}\\\\\sf x=\log_2\bigg(\dfrac{704}{81}\bigg)\end{array}}[/tex]