333
punti
Livello 1
Con
* 2^(x - 1) = 2^x/2
* (√3)^(x + 1) = (√3)*(√3)^x
* (1/2)^x = 1/2^x
si ha
* (2^(x - 1))*(√3)^(x + 1)/3 < (1/2)^x ≡
≡ (2^x/2)*(√3)*(√3)^x/3 < 1/2^x ≡
≡ (2^x)*(√3)^x/(2*√3) < 1/2^x ≡
≡ (2^x)*(2^x)*(√3)^x < 2*√3 ≡
≡ (2*2*√3)^x < 2*√3 ≡
≡ log(4*√3, (4*√3)^x) < log(4*√3, 2*√3) ≡
≡ x < ln(2*√3)/ln(4*√3) = ln(12)/ln(48) ~= 0.6418955 ~= 0.64
CONTROPROVA al link
http://www.wolframalpha.com/input?i=%282%5E%28x-1%29%29*%28%E2%88%9A3%29%5E%28x--1%29%2F3%3C%281%2F2%29%5Ex
57798
punti
Genius I