Answer:
[tex]x = \dfrac{24}{25}[/tex]
Step-by-step explanation:
In the equation
[tex]1296^{5x-11}=7776^{-x-4}[/tex]
the bases can be rewritten to give
[tex](6^4)^{5x-11}=(6^5)^{-x-4}[/tex]
which simplifies to
[tex]6^{4(5x-11)}=6^{5(-x-4)}[/tex]
[tex]6^{(20x-44)}=6^{(-5x-20)}[/tex]
taking [tex]log_6[/tex] of both sides gives
[tex]{(20x-44)}={(-5x-20)}[/tex]
and solving for [tex]x[/tex] gives
[tex]\boxed{x = \dfrac{24}{25}}[/tex]
which is our solution.
