Question

0.5log10^64 _log10^2+log10^5^2

Answer 1

1/2 log 10^64 = 1/2 * 64 = 32

log 10^2 = 2
log 10^5^2 = log10^25 = 25
so the sum is 32-2+25 = 55

unless you meant, in your somewhat unusual notation for logs base 10
1/2 log64 = log8
log 5^2 = log25
and now we have
log8-log2+log25 = log(200/2) = log100 = 2