Number of integral solution of equation `5^(log_5^2 x+x^(log_5x))=1250` is

If p and q are solutions of the equation 5^((log_(5)^(2) x))+x^(log_(5)x)=1250 then log_(q)p has the value equal to

If x_1 and x_2 (x_2gtx_1) are the integral solutions of the equation (log_5x)^2+log_(5x)(5/x)=1 , , the value of |x_2-4x_1| is

If x_1 and x_2 (x_2gtx_1) are the integral solutions of the equation (log_5x)^2+log_(5x)(5/x)=1 , , the value of |x_2-4x_1| is

If x in R, then number of real solution of the equation 2^(x)+2^(-x)=log_(5)24 is

If x_(1) and x_(2) are the solutions of the equation 5^((log_(5)x)^(2))+x^(log_(5)x)=1250, then x_(1)*x_(2) is equal to

If alpha and beta are solutions of the equation 5^(log_(5)2)+x^(log_(5)x)=1250; then log_(beta)alpha equals :

Find the number of integral solution of the equation log_(sqrt(x))(x+|x-2|)=log_(x)(5x-6+5|x-2|)