Question

Determinati x din egalitatea:

3²ˣ⁺⁵ - 3²ˣ⁺³ - 3²ˣ⁺¹ - 3²ˣ = 1908
Va rogg:)))))))))

Answer 1

$3^{2x+5}-3^{2x+3}-3^{2x+1}-3^{2x}=1908 \\\\ 3^{2x}* 3^5-3^{2x}*3^3-3^{2x}*3-3^{2x}=1908 \\\\ 3^{2x}(243-27-3-1)=1908 \\\\ 3^{2x}* 212=1908 \ \ \ |:212 \\\\ 3^{2x}=9 \\\\ 3^{2x}=3^2 \\\\ 2x=2 \ \ \ |:2 \\\\ \boxed{x=1}$

Answer 2

3²ˣ * 3⁵ - 3²ˣ * 3³ - 3²ˣ * 3 - 3²ˣ = 2² * 3² * 53
3²ˣ(3⁵ - 3³  - 3 - 1) = 2² * 3² * 53
3²ˣ * (243 - 27 - 3 - 1) =  2² * 3² * 53
3²ˣ * 212 = 2² * 3² * 53           | :4
3²ˣ * 53 = 3² * 53           | :53
3²ˣ = 3²
2x = 2
x = 1