The concept is "maximum value of 10 digit number represented by 64 digits should be equal to x digits number in base 2."
For maximum value with 64 digits, each digit must be 9. This is given by $10^{64} - 1$. Similarly, maximum value of $x$ digits in binary is $2^x - 1$.
So $10^{64}-1 = 2^x-1$
$10^{64} = 2^x$
$x = 64 . \log_2 10$
$x = 64 \times 3.32 \approx 213.$