Log10 xf = log10 xo + n log10 0.5. write an expression to find n.

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