Question

Please help solve this equation!!

Answer 1

\[9^{x-1}= 27^{0.5x}\]

Answer 2

gimmick is to rewrite both sides with the same base, namely \(3\)

Answer 3

since \(9=3^2\) the left is
\[\huge (3^2)^{x-1}=3^{2(x-1)}=3^{2x-2}\]

Answer 4

the right is \(27=3^3\) so
\[\huge (3^3)^{.5x}=3^{1.5x}\]

Answer 5

all that is left to do is solve
\[2x-2=1.5x\] and you are done

Answer 6

thank you so much!!