Question

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

Answer 1

$3^x=a, left { {{y=2} atop {x=2}} right. 2^x=b\a^2+b^2=2.5ab\a^2-2.5ab+b^2=0\D=6.25b^2-4b^2=2.25b^2\a_1={2.5b+1.5bover2}=2bleft[begin{array}{ccc}1&2&3\4&5&6\7&8&9end{array}right]\a_2={2.5b-1.5bover2}={bover2}\ left [ {{3^x=2*2^x} atop {3^x=2^{x-1}}} right.\ left [ {{1.5^x=2} atop {1.5^x={1over2}} right.\left [ {{x=log_{1.5}2} atop {x=log_{1.5}{1over2}}} right.\x=pm log_{1.5}2$

Ответ: $x=pm log_{1.5},2$