Write both sides as powers of 8, then simplify:
[tex]8^{\log_86x}=8^{\log_82+\log_8(x-4)}=8^{\log_82}8^{\log_8(x-4)}[/tex]
[tex]\implies6x=2(x-4)[/tex]
[tex]\implies6x=2x-8[/tex]
[tex]\implies4x=-8[/tex]
[tex]\implies x=-2[/tex]
However, on the left hand side, this would mean we'd have, [tex]\log_8-12[/tex], which is undefined (assuming the real-valued logarithm), so this equation has no real solution.
