Question

Determinati x din egalitatea: 4 la puterea 5 ori 2 la puterea 14 ori x + 8 la puterea 9 = 4 la puterea 14.Multumesc anticipat!

Answer 1

$4^5\cdot2^{14}\cdot x+8^9=4^{14} \ \Leftrightarrow 2^{10}\cdot2^{14}\cdot x +2^{27} = 2^{28}$
 
$\Leftrightarrow 2^{24} \cdot x = 2^{28} - 2^{27} \Leftrightarrow 2^{24}\cdot x = 2^{27}(2-1) \Leftrightarrow x=2^{27} :2^{24} =2^3 = 8$