Answer:
x = 3
Step-by-step explanation:
using the rule of exponents
[tex]4^{x}[/tex] = [tex](\frac{1}{2}) ^{x-9}[/tex]
[tex](2^2)^{x}[/tex] = [tex](2^{-1}) ^{x-9}[/tex]
[tex]2^{2x}[/tex] = [tex]2^{-1(x-9)}[/tex] = [tex]2^{9-x}[/tex]
suince the bases on both sides are equal, then equate the exponents
2x = 9 - x ( add x to both sides )
3x = 9 ( divide both sides by 3 )
x = 3
