What is the big number?

102^100 105^94 What is bigger?

There are a few ways of doing this.

You can use a high powered calc like asinus did.

You can use log.

Here is another way.

105/120=1.02941765

\(102^{100} = 102^6 \times 102^{94} \\ 105^{94}=(1.02941765*102)^{94}=1.02941765^{94} \times 102^{94}=15.25\times 102^{94}\\\)

102^6 is obviously bigger than 15.25

so

\(102^{100}>105^{94}\)

102^100 105^94 What is bigger?

\(102^{100} > 105^{94}\)

\(7.24464611827\times 10^{200}>9.81282632821\times 10^{189}\)

  !

Write   102^100   as  100 log 102   and  105^94  as  94 log 105

100 log 102  .....   94 log 105   ???       rearrange as

100/94     .......  log 105/log 102    ????

50/47   ...........  ≈ 1.006   ????

1.0638  >  ≈ 1.006

So

102^100  >   105^94