Given the exponent equation 2^(3x-1) = 16.

We need to find the values of x that satisfies the equation.

First we will simplify the right side.

We know that 16 = 4*4 = 2*2*2*2 = 2^4

Then we will rewrite into the equation.

==> 2^(3x-1) = 2^4

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

==> 3x-1 = 4

We will solve by adding 1 to both sides.

==> 3x = 5

Now we will divide by 3.

**==> x = 5/3.**

We have to solve 2^(3x - 1) = 16 for x.

2^(3x - 1) = 16

=> 2^(3x - 1) = 2^4

as the base is the same, we can equate the exponent

=> 3x - 1 = 4

=> 3x = 5

=> x = 5/3

**The required solution for x is x = 5/3**

The value of x has to be determined given that 2^(3x-1) = 16.

Now looking at both the sides neither the base nor the exponent is equal. But notice that 16 can be written as a power of 2 as 16 = 2^4

Now substituting this in the equation 2^(3x - 1) = 16 gives:

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

As the base 2 is same on both the sides, the exponent can be equated and the equation derived solved for x.

3x - 1 = 4

3x = 5

x = 5/3

The required solution of the equation is x = 5/3