`log_((sqrt(2)+1))(sqrt(2)-1)=`

The value of log_((sqrt(2)-1))(5sqrt(2)-7) is :

which of the following are positive and negative: (i) log _(sqrt(3))sqrt(2) (ii) log_(4)((sqrt(2)+1)/(sqrt(2)-1))

Prove that : int_(0)^(pi//2)(x)/(sin x +cos x)dx= (pi)/(4sqrt(2)) log |(sqrt(2)+1)/(sqrt(2)-1)|

The area bounded by the curve y=secx , the x-axis and the lines x=0 and x=pi/4 is (A) log(sqrt(2)+1) (B) log(sqrt(2)-1) (C) 1/2log2 (D) sqrt(2)

Find the sum of the squares of all the real solution of the equation 2log_((2+sqrt(3)))(sqrt(x^(2)+1)+x)+log_((2-sqrt(3)))(sqrt(x^(2)+1)-x)=3

(ii) log_(sqrt(5)+1)(6+2sqrt(5))

The value of 2(log_(sqrt(2)+1)sqrt(3-2sqrt(2))+log_((2)/(sqrt(3+1)))(6sqrt(3)-10)) is

The value of int(log_(e)(x+sqrt(x^2)+1))/(sqrt(x^(2)+1))dx is

evaluate 5^(log_((1)/(3))((1)/(2)))+log_(sqrt(2))((4)/(sqrt(7)+sqrt(3)))+log_((1)/(2))((1)/(10+2sqrt(21)))

5^(log_((1)/(5))((1)/(2)))+log_(sqrt(2))((4)/(sqrt(7)+sqrt(3)))+log_((1)/(2))((1)/(10+2sqrt(21)))