Value of 361 raised to power log 5 to the base 19

If log(xy^(3))=1 and log(x^(2)y)=1, then the value of xy is equal to (where base of the logarithm is 32)

If N= anti log _(3)(log_(6)(antilog_(sqrt(5))(log_(5)(1296))) then the characteristic of log N to the base 2 is equal to

If x=log2 and y=log3, then a+bx+cy=[log1+log(1+3)+log(1+3+5)+....+log(1+3+5+....,+19)]- 2 [log1+log2+log3+.....+log7], where a,b and c are positive integers. The value of 2a+3b+5c is equal to (where log a=log_(10)a)

Inequality Based Questions || e raised to power x Based Inequality

If sum of the integral values of x satisfying the equation |x-1|^(log^(2)x-1log^(2))=|x-1|^(3) is N, then find characteristic of logarithm of N to the base 5.

if log 15 base 16=a and log 18 base 12=b then show that log 24 base 25=(5-b)/(16a-8ab-4b+2)

Let L denote antilog 320.6 and M denote the number of positive integers which have the characteristic 4, when the base of log is 5, and N denote the value of 49^((1-log_(7)2))+5^(-log_(5)4) Find the value of (LM)/(N) .