Write the functionf(x) =x1−xas a power series about the pointx= 0. Find theradiusand intervalof convergence of the power series (check the endpoints) g

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: