Log 2 with base 5, log 2 raised to x with base 5 and log 17/2+2 raised to x-1 with base 5 are in AP then find x

As per the question,log2 + log[(17+2^x)/2] =2log(2^x-3)[ALL LOGS ARE TO THE BASE 5]=> log2+log(17+2^x)-log2=2log(2^x-3)=> log(17+2^x)=log(2^x-3)²LET 2^x=a=> 17+a=a²+9-6a=> a²-7a-8=0=> a=(-1) OR a=8=> 2^x=-1 (not possible) OR=> 2^x=3=> x=3Hope it helps you!With regards,SARTHAK