Question

(√6)^8x = 216^x -3

Answer 1

\[(\sqrt 6)^{8x} = 216^{x-3}\]
\[(6^{1/2})^{8x} = (6^3)^{x-3}\]
\[6^{8x/2} = 6^{3(x-3)}\]
\[6^{4x} = 6^{3x - 9}\]
4x = 3x - 9
solve for x now

Answer 2

x = -9.
But when you made the bases the same, I completely don't understand that..

Answer 3

\[\sqrt{6} = 6^{1/2}\]
do you agree?

Answer 4

yes.

Answer 5

\[216 = 6^3\]
agree?

Answer 6

ohh I see what you did there now. The ^1/2 threw me off in the beginning

Answer 7

Thanks :)

Answer 8

haha you're welcome :)

Answer 9

wait uhh i still don't get it. how does 6=6 1/2?