Plz Help!!!?

Question

if b > or equal to 1 , Show that e^b > or equal to b^e I ried to differentiate but it didn't work

if b is bigger than or equal to 1 , Show that e^b is bigger than or equal to b^e I tried to differentiate but it didn't work !!

if i multiply both sides with ln then ill have b>eln|b| n if i derive -----)1>e/b is this correct

e>b/ln|b|
d(x/ln(x)) = 0
ln|x|-1>=0
derive again-------)1/x>=0--------))1>0 which is true !!

Answer 1

e^b >= b^e [b>1]
lne^b >= lnb^e
blne >= elnb
b>= elnb
b/lnb >= e
If you treat b/lnb as a function, take the derivative and set = 0 you will find it has a minimum value of e, so e^b >= b^e

Answer 2

Think of it this way: e is a constant number, and b is a variable. Therefore, e^b can get really big really fast because the exponent grows with larger values of b. However, in b^e, the base grows which does not make for as steep of growth in the final value.

Answer 3

use induction. I replied to this question
prove for a base case b=1
e^b > or equal to b^e is true.
now that you have for some k : e^k > or equal to k^e (you know that it is true)
prove e^(k+1) > or equal to (k+1)^e
what you want to do is re-order it so you have e^k > or equal to k^e and some other terms and then you will see that e^(k+1) > or equal to (k+1)^e also holds true. (this is assuming that these are integers)

Answer 4

What your saying is, if B is greater than or equal to 1, show how its.... E is = to B, or show how B is = to E

B = 1
Or B = 2
Or E = 1
Or E = 2

I worked it out myself, if you dont believe me, atleast I tried unlike some other people.... hope this helps ^_^

Answer 5

Try the second derivitive.

Answer 6

i don't know