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

Simplify ( i) 3^(sqrt(log_(3)(2)))-2sqrt(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

Simplify: 2^((log)_3 5)-5^((log)_3 2)

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