# Log expansions

#### mathelord

How Do I Find The Logarithmic Expansions Of Log[x],i Mean The Series Of Log[x].it Is Urgent

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#### mustafa

The series expansion of any function can be obtained by Taylor's series expansion:
f(x)=f(a)+(x-a)f'(a)+(x-a)^2f"(a)/2!+(x-a)^3f"'(a)/3!+...

Using the above formula, any function can be expanded in terms of powers of (x-a), provided that all derivatives of f(x) are defined at x=a.

Note: logx can not be expanded in terms of powers of x, because the derivatives of logx are not defined at x=0.

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#### lurflurf

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mustafa said:
Note: logx can not be expanded in terms of powers of x, because the derivatives of logx are not defined at x=0.
I think you mean log x cannot be expanded about zero in a series of nonnegative powers.

#### MaxwellPhill

example can be done via the log(1+x) series |x|<1

x-x^2/2+x^3/3....

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