radicand equation of 1/2n+3=3

There is an index of 4
1/2n+3=3x3x3x3
1/2n +3=81
1/2n=81-3
1/2n=78
n=39

almost.

If 2n=78, n=29
If 1/2 n = 78, n = 156

We customarily use a caret, as in 3^4, to indicate powers.