[" Solution of the equation "log_(5)(root(3)(5)+125)=],[(log_(5)6+1+(1)/(2x))" is "]

If log_(5)(5^((1)/(x))+125)=log_(5)6+1+(1)/(2x), then x=

Sum of all the solutions of the equation 5^((log_(5)7)^(2x))=7^((log_(7)5)^(x)) is equal to

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 x_(1) and x_(2) are solution of the equation log_(5)(log_(64)|x|+(25)^(x)-(1)/(2))=2x , then

If x_(1) and x_(2) are solution of the equation log_(5)(log_(64)|x|+(25)^(x)-(1)/(2))=2x , then

If x_(1) and x_(2) are solution of the equation log_(5)(log_(64)|x|+(25)^(x)-(1)/(2))=2x , then

Number of solutions of the equation (1)/(2)log_(sqrt(3))((x+1)/(x+5))+log_(9)(x+5)^(2)=1 is -