Question

Determinați numărul natural x: 2^x-2000+2^x-2001+2^x-2002=14​

Answer 1

Răspuns:

$x \in \varnothing$

Explicație pas cu pas:

$2^x - 2000 + 2^x - 2001 + 2^x - 2002 = 14\\\\3\cdot 2^x = 14 + 2000 + 2001 + 2002\\\\ 3\cdot 2^x = 6017\\\\2^x = \frac{6017}{3}\\\\x = log_2(2^x) = log_2(\frac{6017}{3}) = log_2(6017) - log_2(3) \notin \mathbb{N} \\\\\implies x \in \varnothing$