Question

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)) = ?

Answer 1

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