The given equation is:
[tex]2^{12-2x}=16[/tex]Apply logarithm to both sides:
[tex]\log 2^{12-2x}=\log 16[/tex]Apply the properties of logarithms:
[tex](12-2x)\log 2=\log 16[/tex]Divide both sides by log2:
[tex]\begin{gathered} \frac{(12-2x)\log2}{\log2}=\frac{\log 16}{\log 2} \\ \text{Simplify} \\ 12-2x=\frac{\log 16}{\log 2} \end{gathered}[/tex]And:
[tex]\begin{gathered} \log _ax=\frac{\log _bx}{\log _ba} \\ \text{Then:} \\ \frac{\log _{10}16}{\log _{10}2}=\log _216=4 \end{gathered}[/tex]Thus:
[tex]\begin{gathered} 12-2x=4 \\ -2x=4-12 \\ -2x=-8 \\ x=\frac{-8}{-2} \\ x=4 \end{gathered}[/tex]The answer is x=4.