Simplify (i) `3^(sqrt(log_3(2))`-`2^(sqrt(log_2(3)`

The value of expression 3^sqrt(log_(27) 8)-2^sqrt(log_(32)243)-5^sqrt(log_(625) 81)+3^sqrt(log_9 25)+(sqrt2)^(log_2 9)+3^(log_4 25)-5^(log_4 9) , is less then

Product of all the solution of equation x^(log_(10)x)=(100+2^(sqrt(log_(2)3))-3^(sqrt(log_(3)2)))x is

Product of all the solution of equation x^(log_(10)x)=(100+2^(sqrt(log_(2)3))-3sqrt(log_(3)2))x is

Simplify: ((sqrt 3)/2 + i/2)^3

Calculate : (iii) log_(3)(sqrt6)+log_(3)(sqrt(2/3))-log_(3)log_(3)(9)

(log_(3)243)/(log_(2)sqrt(32))

If P =3^sqrt(log_(3)2)-2^(sqrt(log_(2)3))and Q=log_(2)log_(3)log_(2)log _(sqrt(3))81, then

If P =3^sqrt(log_(3)2)-2^(sqrt(log_(2)3))and Q=log_(2)log_(3)log_(2)log _(sqrt(3))81, then

value of 7^[{sqrt(log_7 3)+ sqrt(log_14 3)}*2^sqrt(log_14 3)]/3^{sqrt(log_3 7)+sqrt(log_3 14)) is equal to:

Find the value of x satisfying the equation,sqrt((log_(3)3sqrt(3)x+log_(x)3sqrt(3)x)*log_(3)x^(3))+sqrt(((log_(3)(3sqrt(x)))/(3)+(log_(x)(3sqrt(x)))/(3))*log_(3)x^(3))=2