Question

Log27+log27(x+8) = 2/3

Answer 1

using log A + log B = log (A+B)

log 27 + log 27(+8) = 2/3
log [27*27(x+8)] = 2/3
10^(2/3) = 729(x+8)
x+8 = 10^(2/3) / 729
x = 10^(2/3) / 729 - 8 = ....

I have a feeling you have a typo.
Is the 27 the base of the logarithm?
If so, then log₂₇ makes no sense.
Come back with the proper question.