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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

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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.

Approved by eNotes Editorial Team