2. а) 9²ˣ - 3²ˣ⁺² + 14 = 0
3⁴ˣ - 9·3²ˣ + 14 = 0
Пусть t = 3²ˣ, t > 0.
t² - 9t + 14 = 0
t² - 7t - 2t + 14 = 0
t(t - 7) - 2(t - 7) = 0
(t - 2)(t - 7) = 0
t = 2; 7
Обратная замена:
3²ˣ = 2
2x = log₃2
x = 0,5log₃2
x = log₉2
или
3²ˣ = 7
3x = log₃7
x = 0,5log₃7
x = log₉7
Ответ: log₉2; log₉7.
3. б) log₁₅²3 + log₁₅5·log₁₅45 = log₁₅²3 + log₁₅(15/3)·log₁₅(15·3) = log₁₅²3 +
+ (log₁₅15 - log₁₅3)(log₁₅15 + log₁₅3) = log₁₅²3 + log₁₅²15 - log₁₅²3 = log₁₅²15 = 1