Which is smaller? 2 or `(log_(("e"-1))2+log_2(e-1))`

Which is smaller 2 or (log_pi 2+log_2 pi)

Solve log_(e)(x-a)+log_(e)x=1.(a>0)

Which one is greater: cos(log_e theta)or log_e(costheta) if -pi/2ltthetaltpi/2

If int(2^(1setminusx))/(x^2)\ dx=k\ 2^(1setminusx)+C , then k is equal to -1/((log)_e2) (b) (log)_e2 (c) -1 (d) 1/2

Comprehension 2 In comparison of two numbers, logarithm of smaller number is smaller, if base of the logarithm is greater than one. Logarithm of smaller number is larger, if base of logarithm is in between zero and one. For example log_2 4 is smaller than (log)_2 8\ a n d(log)_(1/2)4 is larger than (log)_(1/2)8. Identify the correct order: (log)_2 6 (log)_3 8> log_3 6>(log)_4 6 (log)_3 8>(log)_2 6> log_3 6>(log)_4 6 (log)_2 8<(log)_4 6

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

The value of 1+(log_(e)x)+(log_(e)x)^(2)/(2!)+(log_(e)x)^(3)/(3!)+…infty

Evaluate lim_(hto0) (log_(e)(1+2h)-2log_(e)(1+h))/(h^(2)).

Find the value of lim_(xto0^(+)) (3(log_(e)x)^(2)+5log_(e)x+6)/(1+(log_(e)x)^(2)).

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)