Prove that the number x that satisfy 2 ^ x = 5 is not a number rasional.
Favorites|Homepage
Subscriptions | sitemap
HOME > Mathematics > Prove that the number x that satisfy 2 ^ x = 5 is not a number rasional.

Prove that the number x that satisfy 2 ^ x = 5 is not a number rasional.

[From: ] [author: ] [Date: 11-08-17] [Hit: ]
s. one extra detail: x is positive, so if it was rational there would exist positive a and b. (The contradiction isnt so obvious if negative powers are allowed).......
Prove that the number x that satisfy 2 ^ x = 5 is not a number rasional.

please help me

-
Ususally you solve a problem like this by assuming x is the rational a/b, where a and b are integers, and trying to find a contradiction.

2 ^(a/b) = 5
=> (2^a) ^ (1/b) = 5
=> 2^a = 5^b

See the contradiction? (Remember a and b are integers).

EDIT: p.s. one extra detail: x is positive, so if it was rational there would exist positive a and b. (The contradiction isn't so obvious if negative powers are allowed).
1
keywords: that,not,is,satisfy,Prove,number,rasional,the,Prove that the number x that satisfy 2 ^ x = 5 is not a number rasional.
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .