I don't have any issue of how to solve these problems, please help me teacher.

1.Log4^1/8=?
2.log100^0.001=?
3.log8^0.00625=?

You are using the rule

log (x^a) = a log x
e.g. #1
log (4^(1/8) )
= (1/8)log 4 , use your calculator to get an approximate answer.

do the other two the same way,
btw, for #2, you will get an exact answer