Input
log(4, X + 1)
Exact result
log(X + 1)/log(4)
Alternate form assuming X>0
log(X + 1)/(2 log(2))
Root
X = 0
Series expansion at X=-1
log(X + 1)/log(4) + O((X + 1)^6)
(generalized Puiseux series)
Series expansion at X=0
X/log(4) – X^2/log(16) + X^3/log(64) – X^4/log(256) + X^5/log(1024) + O(X^6)
(Taylor series)
Series expansion at X=∞
log(X)/log(4) + 1/(X log(4)) – 1/(X^2 log(16)) + 1/(X^3 log(64)) – 1/(X^4 log(256)) + 1/(X^5 log(1024)) + O((1/X)^6)
(generalized Puiseux series)
Derivative
d/dX(log(4, X + 1)) = 1/(X log(4) + log(4))
Indefinite integral
integral log(1 + X)/log(4) dX = ((X + 1) log(X + 1) – X)/log(4) + constant
(assuming a complex-valued logarithm)
Definite integral
integral_(-1)^0 log(1 + X)/log(4) dX~~-0.72134752044…
Alternative representation
log(4, X + 1) = log(1 + X)/log(4)