How to make Maple determine whether the following is a sequence with a rule behind it or just random fractions:

3^893/2^1415, 3^1040/2^1648, 3^2192/2^3474, 3^3776/2^5984, 3^3910/2^6197, 3^5514/2^8739

How should I proceed to convert 2ln(3) -3ln(2)  to trigonometric form in Maple?

Is it possible to construct in Maple the following sequence of ascending fifths?:

3/2, 3^2/2^3, 3^3/2^4, 3^4/2^6, 3^5/2^7, 3^6/2^9, 3^7/2^11, 3^8/2^12 and so on. The result always more than 1 and less than 2.

Given a sequence for example: 8, 32,128,512,2048 and so on. Suppose we do not know it is 2^(2n +1). How to make Maple to find the principle?

In the fraction 3^665/2^x=y, where y is more than 1 and less than 2, I want to know the value of x. What input should I write, please?