8^x+1=3

I have a feeling that you mean

8^(x+1) = 3

if not, then it would be real easy
8^x + 1 = 3
8^x = 2
and we now the cube root of 8 is 2, so
x = 1/3

if 8^(x+1) = 3
log both sides
log 8^(x+1) = log3
(x+1)log8 = log3
x+1 = log3/log8
x = log3/log8 - 1
= appr -.47168