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