3*16^x+2*81^x=5*36^x

Question

3*16^x+2*81^x=5*36^x

Answer 1

3*2^4x+2*3^4x=5*2^2x*3^2x

3*2^4x/(2^2x*3^2x)+2*3^4x/(2^2x*3^2x)=5
3*(2/3)^2x+2*(3/2)^2x=5
(3/2)^2x=t
3/t+2t=5
2t^2-5t+3=0
t1=1
t2=3/2
(3/2)^2x=1
x=0
(3/2)^2x=3/2
x=1/2
ответ х=0 х=1/2