If `log(x^(2) - 21) = 2`, show that x = + 11.

x^(2) log x

x log 2x

Solve for x : (i) log_(10) (x - 10) = 1 (ii) log (x^(2) - 21) = 2 (iii) log(x - 2) + log(x + 2) = log 5 (iv) log(x + 5) + log(x - 5) = 4 log 2 + 2 log 3

If y=log[x+sqrt(x^2+a^2)\ ] , show that (x^2+a^2)(d^2\ y)/(dx^2)+x(dy)/(dx)=0

If log_(2)x + log_(2)x=7 , then =

If log(x^2+y^2)=2tan^(-1)(y/x), show that (dy)/(dx)=(x+y)/(x-y)

If log(x^2+y^2)=2tan^(-1)(y/x), show that (dy)/(dx)=(x+y)/(x-y) .

If y={log(x+sqrt(x^2+1))}^2 , show that (1+x^2)(d^2y)/(dx^2)+x(dy)/(dx)=2 .

If x^(y) y^(x)=5 , then show that (dy)/(dx)= -(log y + (y)/(x))/(log x + (x)/(y))

If "log"_(4)(3x^(2) +11x) gt 1 , then x lies in the interval