Find the number of positive integers not satisfying the inequality $$\log_2(4^x-2(2^x)+17)>5$$
My approach: let $2^x=t$ then inequality is rewritten in form
then I defined the argument
now I don't know how to proceed next.
Also, I tried to remove log from both sides then I get
solving for $t$ I get $$t=-3,5$$
What to do next?