3³ˣ - 8*3ˣ*3² + 5*3⁵*3⁻ˣ = 0 | * 3ˣ [1,7; 2]
3⁴ˣ - 72*3²ˣ +1215 = 0
3²ˣ = t
t² - 72t +1215 = 0
t = 36 +-√(1296 -1215)= 36 +-√81 = 36 +-9
t₁ = 45 t₂ = 27
3²ˣ = 45 3²ˣ = 27
2xlg3 = lg45 2x = 3
x = lg45/lg9 x = 1,5 ( не входит в указанный промежуток)
x = (lg9 +lg5)/lg9=
=1 + lg5/2lg3
x = 1 + lg5/2lg3