`log(x+1)^(x^2)=4log(x+1)`

log x-(1)/(2)log(x-(1)/(2))=log(x+(1)/(2))-(1)/(2)log(x+(1)/(8))

log_(4)(x^(2)-1)-log_(4)(x-1)^(2)=log_(4)sqrt((4-x)^(2))

If 0ltxlt1 , prove that: log(1+x)+log(1+x^2)+log(1+x^4)+… oo=-log(1-x)

Solve for x:(log)_(4)(x^(2)-1)-(log)_(4)(x-1)^(2)=(log)_(4)sqrt((4-x)^(2))

int(log(x+1)-log x)/(x(x+1))dx= (A) log(x-1)log x+(1)/(2)(log x-1)^(2)-(1)/(2)(log x)^(2)+c (B) (1)/(2)(log(x+1))^(2)+(1)/(2)(log x)^(2)-log(x+1)log x+c (C) -(1)/(2)(log(x+1)^(2))-(1)/(2)(log x)^(2)+log x*log(x+1)+c (D) [log(1+(1)/(x))]^(2)+c

Prove that 2 log x-log (x +1)-log (x -1)= 1/x^2+1/(2x^4)+1/(3x^6) +......, where |x|<1.

Solve for x:log_(2)(4(4^(x)+1))*log_(2)(4^(x)+1)=log_((1)/(sqrt(3)))(1)/(sqrt(8))

log(x-1)+log(x-2)lt log(x+2)

If x_n > x_(n-1) > ..........> x_3 > x_1 > 1. then the value of log_(x1) [log_(x2) {log_(x3).........log_(x4) (x_n)^(x_(r=i))}]

log_((3)/(4))log_(8)(x^(2)+7)+log_((1)/(2))log_((1)/(4))(x^(2)+7)^(-1)=-2