Which is bigger: ( 1 + \sqrt{2} )^{ 1 + \sqrt{2} + 10^{-9,000} } (1+√2)1+√2+10−9,000 or ( 1 + \sqrt{2} + 10^{-9,000} )^{ 1 + \sqrt{2} } (1+√2+10−9,000)1+√2 ? If your calculator could actually handle this -- please put it away !! :)
(I have hints available, if necessary.)
(I have hints available, if necessary.)
2 Answers
I think both are equal.
Explanation:
10^-9000->010−9000→0 as its value is negligible.Then
(1+sqrt2)^(1+sqrt2+0)=(1+sqrt2+0)^(1+sqrt2)(1+√2)1+√2+0=(1+√2+0)1+√2 .Otherwise, I was thinking about logarithm concept.
See below.
Explanation:
Calling
both
and
now
and consequently
but
Considering now that