Number series

Question

Find which is the greater, 65¹⁶⁶² or 33¹⁹⁹⁵

Answer 1

their respective natural logarithms are 1662ln65 and 1995ln33.

 

calckulate those values; the one with the larger logarithm indicates which of the original expressions is the greater.

Answer 2

 

65^1662 > 33^1662

 

 

65^1662 * 33^333 > 33^1662 * 33^333 = 33^1995

 

So 33^1995 is larger.

 

 

Note that in scientific notation:

 

65^1662 = 1.15 * 10^3013

   vs

33^1995 = 2.72 * 10^ 3029