What are the steps to solve the equation 9^(x-1) =27*3^x ?

The first important step is to create matching bases both
sides.

Since 9 is a power of 3, we'll write it
as:

9 = 3^2

Also 27 is a power of
3:

27 = 3^3

Now, we'll apply the
multiplication rule of 2 exponentials that have matching
bases:

3^3*3^x = 3^(3 + x)

We'll
re-write the equation:

3^2(x-1) = 3^(3 +
x)

Since the bases are matching, we'll apply one to one
rule:

2(x-1) = (3 + x)

We'll open the
brackets:

2x - 2 = x + 3

We'll move all
terms to one side:

2x - x - 2 - 3 =
0

We'll combine like terms:

x - 5 =
0

We'll add 5:

x =
5

The requested solution of the given equation is x =
5.