Question

Alfati x din urmatoarele relaţii
a)X^4=81
b)2^X < 31
c)3^x+1 <243
d)2^x<3^x
e)3^x>5^x
( ^ inseamna la puterea)

Answer 1

[tex]a) \\x^4=81=3^4\\ x=4\\b)\\ 2^x\ \textless \ 31\ \textless \ 32=2^5\\ x\ \textless \ 5\\ x\in\{0,1,2,3,4\}\\ c)\\3^x\ \textless \ 242\ \textless \ 243=3^5\\ x\ \textless \ 5\\ x\in\{0,1,2,3,4\}\\ d) 2^x\ \textless \ 3^x|:2^x\\ (\frac{3}{2})^x\ \textgreater \ 1\\ 1,5^x\ \textgreater \ 1\\ e)\\ 3^x\ \textgreater \ 5^x|:5^x\\ (\frac{3}{5})^x\ \textgreater \ 1\\ 0,6^x\ \textgreater \ 1\ imposibil \ in \ N [/tex]