Converting a number from base $b^l$ to $b^k$ takes $O(M(n)logn)$ time, where $M(n)$ is the time it takes to multiply two n-bit numbers, n is the length of the number.
For example, to convert binary to octal (base $2^1$ to $2^3$), the algorithm is easy; group three bits and find their equivalent values paralelly.
But to convert from a base to another base where they're not a power of some common constant, the conversion is tricky. For example binary to decimal.
For that, we need to multiply the bit at $ith$ position with $2^{i-1}$
It'll take $O(M(n)n)$ time.
Since $O(M(n)\equiv O(1)$ //given
It takes $O(n) time$
Can't be done better than $O(n)$, So, Option A.
Intuition
1010011101 to Octal
=> 001 010 011 101
=> 1235
We grouped numbers together, so O(logn)
1010011101 to binary requires each digit to be multiplied by some power of 2. So, O(n)