Question

Solve the following equation for x :

3^x * 27^(-2 x)= 9^(x - 9)

Answer 1

i got x=-18/-7

Answer 2

We have
\[3^x \times 27^{-2x} = 9^{(x-9)}\]
We know
\[9=3^2\ and\ 27=3^3\]
so
\[3^x \times (3^3)^{-2x}= (3^2)^{x-9}\]
we get now
\[3^x \times 3^{-6x}=3^{-2x-18}\]
So we get
\[3^{x-6x}=3^{-2x-18}\]
equating powers both sides, we get
\[ x-6x=-2x-18\]
or
\[-3x=-18\]
or
\[x=6\]

Answer 3

wait i got x-6x=2x-18
then -5x=2x-18
-7x=-18
x= -18/-7

Answer 4

Sorry I made mistake, you're right. I don't know how I brought a minus:( Sorry

Answer 5

lol thats the same mistake i made on my last test!