Precalculus
posted by jh on .
PLEASE HELP ME WITH THESE QUESTION AS MUCH AS POSSIBLE!!
Evaluate without a calculator. Give exact answers:
a) log(log(10)) = ?
b) square root (log(100))  log(square root(100)) = ?
c) log((square root 10^3)(square root 10^5)(square root 10) = ?
d) 1000^log(3) = ?
e) log(1/log(10square root 10)) = ?

a) log(log10)
= log 1 = 0
b) √log100  log(√100)
= √2  log10
=√2  1
c) log(√10^3√10^5√10)
= log √10^9
= log 10^(9/2)
= (9/2)log10 = (9/1)(1) = 9/2
d) 1000^log3
= ((10)^3)^log3
= 10 ^(3log3)
= 10^(log27)
= 27
e) log (1/log(10√10)
= log 1  log(10√10)
= 0  log(10√10)
= log(10√10)
= (log10 + log(√10)
= (1 + 1/2_
= 3/2