We can rewrite the right side of the equation as [tex]32^{x-4}=32^{-2}[/tex].
Therefore, we have [tex]32^{-2} = \frac{1}{32^2}[/tex].
Since [tex]32=2^5[/tex], we have [tex]32^{-2} = (2^5)^{-2} = 2^{-10}[/tex].
So the equation becomes [tex]2^{-10} = 2^{x-4}[/tex].
By comparing the exponents, we get [tex]-10=x-4[/tex].
Solving for [tex]x[/tex], we find [tex]x = -6[/tex].
We can rewrite the right side of the equation as [tex]32^{x-4}=32^{-2}[/tex].
Therefore, we have [tex]32^{-2} = \frac{1}{32^2}[/tex].
Since [tex]32=2^5[/tex], we have [tex]32^{-2} = (2^5)^{-2} = 2^{-10}[/tex].
So the equation becomes [tex]2^{-10} = 2^{x-4}[/tex].
By comparing the exponents, we get [tex]-10=x-4[/tex].
Solving for [tex]x[/tex], we find [tex]x = -6[/tex].