Question

(512)power x+1 - 1024 =0

Answer 1

so we know that 1024=2^10 and 512=2^9

so2^9x+9=2^10

9x+9=10

x=1/10

Answer 2

here is your answer friend:
2^9x+9=1024. (512^x+1-1024=0 and ^ is the power ok)
=} 2^9x+9=2^10
=} 9x+9=10
=}9x=10-9
=}x=1/9

hope it helps you a lot.
thank you very much