If `n >1,t h e np rov et h a t` `1/((log)_2n)+1/((log)_3n)++1/((log)_(53)n)=1/((log)_(53 !)n)dot`

let N =(log_(3) 135/log_(15) 3) - (log_(3) 5/log_(405) 3)

Prove that 1/3<(log)_(10)3<1/2dot

In a binomial distribution B(n , p=1/4) , if the probability of at least one success is greater than or equal to 9/(10) , then n is greater than (1) 1/((log)_(10)^4-(log)_(10)^3) (2) 1/((log)_(10)^4+(log)_(10)^3) (3) 9/((log)_(10)^4-(log)_(10)^3) (4) 4/((log)_(10)^4-(log)_(10)^3)

If 3^x=4^(x-1) , then x= (2(log)_3 2)/(2(log)_3 2-1) (b) 2/(2-(log)_2 3) 1/(1-(log)_4 3) (d) (2(log)_2 3)/(2(log)_2 3-1)

The value of N=((log)_5 250)/((log)_(50)5)-((log)_5 10)/((log)_(1250)5) is...........

Solve x^((log)_y x)=2a n dy^((log)_x y)=16

If a >1,b >1 and c >1 are in G.P. then show that 1/(1+(log)_e a),1/(1+(log)_e b), a n d1/(1+(log)_e c) are in H.P.

A value of C for which the conclusion of Mean Value Theorem holds for the function f(x)""=""(log)_e x on the interval [1, 3] is (1) 2(log)_3e (2) 1/2""(log)_e3 (3) (log)_3e (4) (log)_e3

Which of the following numbers are positive/negative? (a) (log)_2 7 (b) (log)_(0. 2)3 (c) (log)_(1//3)(1/5) (d) (log)_4 3 (e) (log)_2((log)_2 9)

IfI_n=int_0^1x^n(tan^(-1)x)dx ,t h e np rov et h a t (n+1)I_n+(n-1)I_(n-2)=-1/n+pi/2