Question

Determinati numarul natural ''x'' din urmatoarele egalitati :
18 la puterea x+2: 2⁵ = 3 ¹°

Answer 1

$18^{x+2}:2^5=3^{10}\\ 18^x*18^2:2^5=3^{10}\\ 18^x*(3^2*2)^2:2^5=3^{10}\\ 18^x*3^4*2^2:2^5=3^{10}\\ 3^{2x}*2^{x}*2^2:2^5=3^6\\ 3^{2x-6}*3^6*2^{x-3}*2^5:2^5=3^6\\ 3^{2x-6}*2^{x-3}=1\\ 3^{2x}:3^6*2^{x}:2^3=1\\ (3^{2}*2)^x:729:8=1\\ 18^{x}:5832=1\\ 18^{x}=5832\\18^{x}=18^3=\ \textgreater \ x=3$