How many digits are in the usual base 10 representation of 3

How many digits are in the usual base 10 representation of 3^2000?

Solution

The base ten representation of 3^2000 is :

1747871251722651609659974619164660570529062487435188517811888011810686266227275489291486469864681111075608950696145276588771368435875508647514414202093638481872912380089977179381529628478320523519319142681504424059410890214500500647813935818925701905402605484098137956979368551025825239411318643997916523677044769662628646406540335627975329619264245079750470862462474091105444437355302146151475348090755330153269067933091699479889089824650841795567478606396975664557143737657027080403239977757865296846740093712377915770536094223688049108023244139183027962484411078464439516845227961935221269814753416782576455507316073751985374046064592546796043150737808314501684679758056905948759246368644416151863138085276603595816410945157599742077617618911601185155602080771746785959359879490191933389965271275403127925432247963269675912646103156343954375442792688936047041533537523137941310690833949767764290081333900380310406154723157882112449991673819054110440001

Which is INFINITY

the numbe rof digits in this are : 949