`x^(log_5 x) > 5` implies `x in `

If a gt 1, x gt 0 and 2^(log_(a)(2x))=5^(log_(a)(5x)) , then x is equal to

int (1)/( x sqrt( (log x)^(2) - 5 ) ) dx is

If log_(e)5 , log_(e)(5^(x) - 1) and log_(e)(5^(x) - 11/5) are in A.P., then the values of x are

int (e^(6 log x) - e ^(5 log x))/( e^(4 log x) - e^(3 log x)) dx

int(e^(6 log x) - e^(5 log x))/(e^(4 log x) - e^(3 log x)) dx ……………. .

The value of x in the expression (x+x^((log)_(10)x))^5 if third term in the expansion is 10,00,000 is/are a. 10 b. 100 c. 10^(-5//2) d. 10^(-3//2)

(1)/(x log x log (log x ))

Find the derivatives of the following : y = x^(log x) + (log x )^(x)