Question

9^(x)+4^(x)=2,5*6^(x) Помогите решить уравнение!

Answer 1

$3^x=a, \left \{ {{y=2} \atop {x=2}} \right. 2^x=b\\a^2+b^2=2.5ab\\a^2-2.5ab+b^2=0\\D=6.25b^2-4b^2=2.25b^2\\a_1={2.5b+1.5b\over2}=2b\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right]\\a_2={2.5b-1.5b\over2}={b\over2}\\ \left [ {{3^x=2*2^x} \atop {3^x=2^{x-1}}} \right.\\ \left [ {{1.5^x=2} \atop {1.5^x={1\over2}} \right.\\\left [ {{x=log_{1.5}2} \atop {x=log_{1.5}{1\over2}}} \right.\\x=\pm log_{1.5}2$

Ответ: $x=\pm log_{1.5}\,2$