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**

We have to solve 8*2^3x = 4^(x-1) for x.

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

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

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

As the base are equal we can equate the exponent

=> 3+ 3x = 2x - 2

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

=> x = -5

Therefore x = -5

To solve for x : 8*2^3x = 4^(x-1).

=> 8*2^x = (4^x )/4.

=> 8*2^x/4^x = 1/4*8 = 1/8.

=> (2^3/4)^x = 1/32

2^x = 1/32 = 1/2^5 = 2^-5.

=> 2^x = 2^-5.

=> x = -5.

Therefore x = -5.

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