Find the value of x for the equation 8*2^3x = 4^(x-1).

Given the equation:

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

We need to find x
value.

First we need to simplify the
bases.

We know that 8 = 2^3  and 4 =
2^2

==> (2^3)*(2^3x) =
2^2^(x-1)

Now we know that x^a * x^b =
x^(a+b)

Also, we know that x^a^b =
x^(ab)

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

Now that the bases equal, then the powers are
equal too.

==> 3x +3 = 2x
-2

We will combine like
terms.

==> x =
-5