[tex]8^{3x-10}=4^{6x-27}\\\\(2^3)^{3x-10}=(2^2)^{6x-27}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{3(3x-10)}=2^{2(6x-27)}\qquad\text{use distributive property}\\\\2^{(3)(3x)+(3)(-10)}=2^{(2)(6x)+(2)(-27)}\\\\2^{9x-30}=2^{12x-54}\iff9x-30=12x-54\qquad\text{add 30 to both sides}\\\\9x=12x-24\qquad\text{subtract 12x from both sides}\\\\-3x=-24\qquad\text{divide both sides by (-3)}\\\\\boxed{x=8}[/tex]
