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

Question

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

Answer 1

3*4^2x+2*9^2x-5*4^x*9^x=0/9^2x
3*(4/9)^2x-5*(4/9)^x+2=0
(4/9)^x=t
3t²-5t+2=0
D=25-24=1
t1=(5-1)/6=2/3⇒(2/3)^2x=2/3⇒2x=1⇒x=0,5
t2=(5+1)/6=1⇒(4/9)^x=1⇒x=0