Which is bigger: ( 1 + \sqrt{2} )^{ 1 + \sqrt{2} + 10^{-9,000} } or ( 1 + \sqrt{2} + 10^{-9,000} )^{ 1 + \sqrt{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->0 as its value is negligible.Then
(1+sqrt2)^(1+sqrt2+0)=(1+sqrt2+0)^(1+sqrt2) .Otherwise, I was thinking about logarithm concept.
See below.
Explanation:
Calling
both
and
now
and consequently
but
Considering now that