{9}^(?) + {9}^(?) + {9}^(?) = {3}^(2009) what is the value of (?)​

Question

`{9}^(?) + {9}^(?) + {9}^(?) = {3}^(2009)`
what is the value of (?)​

Answer 1

The value of ? is 1004.

Explanation:

I'll use x instead of ?:

`9^x+9^x+9^x=3^(2009)\\3\cdot9^x=3^(2009)\\3\cdot(3^2)^x=3^(2009)\\3\cdot3^(2x)=3^(2009)\\3^(2x+1)=3^(2009)\\2x+1=2009\\2x=2008\\x=1004`