Answer
$24$ bits
Work Step by Step
If a memory has $N$ bytes, then we need enough bits to represent $N$ unique addresses.
Bits in MAR$ = ⌈\log_2(N⌉$
For $N=10,000,000$, we have:
Bits in MAR$ = ⌈\log_2(10,000,000)⌉\approx ⌈23.25⌉ =24$
Minimum bits needed: $24$ bits