4^(x-1) =8*2^3x find x.

Since 8 is a power of 2, we'll write it
as:

8  =2^3

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

2^3*2^3x = 2^(3 +
3x)

We'll re-write the equation, putting 4 =
2^2

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

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

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

We'll
open the brackets:

2x - 2 = 3x +
3

We'll subtract 2x - 2 and we'll apply symmetrical
property:

3x + 3 - 2x + 2 =
0

x + 5 = 0

We'll subtract
5:

x = -5

The
solution of the equation is x = -5.