Can anyone help me with this question:

( [(9^{2x-1}) (3^{3x})^2] / [(27^{x+2})^4] ) = 81^3

I know that x=-19 but I keep getting -1.5 and 8. Step by step would be really appreciated. Thank you.

Okay, put everything to base 3.



Now, work out the powers:



Now, you know that and

Apply this:



Now, simplify:



Equate the powers:



This gives you:

Thanks once again! I now see where I was going wrong. After I worked out the powers, instead of adding the top powers, I was trying to multiply them. (Actually, I think I did try to add them at one point but still ended up with the wrong answer!) Oye! Lol!