[Python] Calculating large numbers in a RAM efficient way

I'm using the following code to calculate modulus for large numbers in a RAM efficient way. This is from another question's answer.

def geom(a,k,n):
"""calculates (1 + a + a^2 + ... + a^(k-1)) mod n)"""
if k <= 2:
return sum(a**i for i in range(k)) % n
else:
m = k//2
b = pow(a,2,n)
g = ((1+a)*geom(b,m,n))%n
return g if k%2 == 0 else (g + pow(a,k-1,n))%n

def f(a,m,n):
""" returns aaaa...a (m times) modulo n"""
k = len(str(a))
r = pow(10,k,n)
return (a*geom(r,m,n))%n


For example,

>>> f(366, 457429086499,164868357)
2013258


I am a novice python user and would like help to modify the above code to calculate:

1. a**m or a (m times) alone
2. log(a) / log(b)
3. a / b**(x-1)

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