Answer:
[tex]\large\boxed{x=-\dfrac{2}{3}}[/tex]
Step-by-step explanation:
[tex]8^x=\dfrac{1}{4}\\==============\\\\8=2^3\\\\\dfrac{1}{4}=\dfrac{1}{2^2}=2^{-2}\\\\===============\\\\(2^3)^x=2^{-2}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{3x}=2^{-2}\iff3x=-2\qquad\text{divide both sides by 3}\\\\x=-\dfrac{2}{3}[/tex]
