Ok, so first we'll start by rearranging the formula.
Subtract log10 Xo from both sides to get
log10 Xf - log10 Xo = nlog10 0.5
Then using log properties you have
log10 (Xf/Xo) = nlog10 0.5
Using another log property we have
log10 (Xf/Xo) = log10 0.5^n
Now we can do
10 ^ (log 10 (Xf/Xo) ) = 10 ^ (log10 0.5^n)
which we evaluate to be
Xf/Xo = 0.5^n
Now we can do
log0.5 (Xf/Xo) = n
