Logarithm Formula
Logarithms are the opposite phenomena of exponential like subtraction is the inverse of addition process, and division is the opposite phenomena of multiplication. Logs “undo” exponentials.
Trivial Identities
logb(1)=0; because b0=1; b>0logb(b)=1; because b1=b
Basic logarithm formulas
logb(xy)=logb(x)+logb(y)logb(b)(xy)=logb(x)−logb(y)logb(xd)=d logb (x)logb(y√x)=logb(x)yc logb(x)+d logb(y)=logb(xcyd)
Changing the base
logb a=logd(a)logd(b)
Addition & Subtraction
logb(a+c)=logb a+logb (1+ca)logb(a−c)=logb a+logb(1−ca)
Exponents
xlog (log(x))log (x)=log (x)