Question 281235
write a rule for log (a)^m. Then use the idea of powers of ten to argue that your rule works for any m and all values of a 0. 
I suppose that log (am)^m = m log a, but how do i use the idea of powers of ten to prove? Please help! 
Note: this problem is meant to help me figure out the power property of log:
log(lower case b) (a^n) = n x log(lower case b)(a)

Show why it makes sense that the log (a)^n = n*log a.

Remember 10^n = 10*10*10...*10 (n 10's).

So we have:

1.) log 10^n = log (10*10*10...*10) (n 10's)

Using the log rule that says log (a*b) = log a + log b then 1.) above becomes:

log 10^n = log 10 + log 10 + log 10 +...+ log 10  (n log 10's) so

log 10^n = n*log 10