Question

解指数方程16^x - 9^(x+1)=8*12^x

Answer 1

16^x-9*9^x=8*12^x

两边除12^x

(4/3)^x-9*(3/4)^x=8

令a=(4/3)^x

则(3/4)^x=1/a

a-9/a=8

a^2-8a-9=0

(a-9)(a+1)=0

因为a=(4/3)^x>0

所以a=9

(4/3)^x=9

x=log(4/3) 9