`1+log_e x+ (log_e x)^2/2!+(log_e x)^3/3!+...=`

Find the range of f(x)=log_e x-((log_e x)^2)/(|log_e x|).

Evaluate: int(e^(5\ (log)_e x)-e^(4\ (log)_e x))/(e^(3\ (log)_e x)-e^(2\ (log)_e x))\ dx

The value of 1-log_(e)2+(log_(e)2)^(2)/(2!)-(log_(e)2)^(3)/(3!)+.. is

The value of 1-log_(e)2+(log_(e)2)^(2)/(2!)-(log_(e)2)^(3)/(3!)+.. is

A : log_(e)3+((log_(e)3)^(2))/(2!)+((log_(e)3)^(3))/(3!)+....=2 R : If x,ainRandagt0" then "a^(x)=1+xlog_(e)a+(x^(2))/(2!)(log_(e)a)^(2)+(x^(3))/(3!)(log_(e)a)^(3)+....

Let x and a be positive real numbers Statement 1: The sum of theries 1+(log_(e)x)^(2)/(2!)+(log_(e)x)^(3)/(3!)+(log_(e)x)^(2)+…to infty is x Statement2: The sum of the series 1+(xlog_(e)a)+(x^(2))/(2!)(log_(e)x))^(2)+(x^(3))/(3!)(log_(e)a)^(3)/(3!)+to infty is a^(x)

Let x and a be positive real numbers Statement 1: The sum of theries 1+(log_(e)x)^(2)/(2!)+(log_(e)x)^(3)/(3!)+(log_(e)x)^(2)+…to infty is x Statement2: The sum of the series 1+(xlog_(e)a)+(x^(2))/(2!)(log_(e)x))^(2)+(x^(3))/(3!)(log_(e)a)^(3)/(3!)+to infty is a^(x)

(d)/(dx)log_(7)(log_(7)x)= (a) (1)/(x log_(e)x) (b) (log_(e)7)/(x log_(e)x) (c) (log_(7)e)/(x log_(e)x) (d) (log_(7)e)/(x log_(7)x)

Find the range of f(x)=log_(e)x-((log_(e)x)^(2))/(|log_(e)x|)