Let x=2^100,〖y=3〗^60 and z=〖10〗^30 . What is the smallest number among the three?

Answer 1

x = 2^100
log x = 100 log 2

y = 3^60
log y = 60 log 3

z = 10^30
log z = 30 log 10

which log is lightest?

Answer 2

I read that as:

x = 2^100 , y = 3^60 , z = 10^30

take log of each one ...
logx = 100log2 = appr 30.103
logy = 60log3 = appr 28.63
logz = 30log10 = 30

logy < logz < logx

y < z < x

so 3^60 is the smallest

(my calculator was actually able to find the values in scientific notation, we could have decided that way)