Answer
$x=−\dfrac{3}{2}$
Work Step by Step
The given expression can be re-written as:
$
4x−3=8^{2x} \\=(2^2)^{x−3}=(2^3)^{2x} \\2^{2(x−3)}=2^{3(2x)} \\2^{2x-6}=2^{6x}$
Apply the rule: $a^m=a^n \longrightarrow m=n$ if $a\ne1,a\ne-1$
$2x−6=6 x\\ 2x=6x+6\\−4x=6\\ x=−\dfrac{3}{2}$
