X pow 100 = 31digit then find x pow 1000= how many digits

• ans- 301
  
  1- 10^1=2 digits
  
  10^2=3 digits......anso on
  
  thf: 10^30=31 digits
  
  now...10^30=x^100
  
  applying log both sides
  
  30 log 10=100 log x
  
  multiply both side by 10
  
  300 log 10=1000 log x
  
  again removing the log from both sides
  
  10^300=x^1000
  
  10^300=301 digits....
• 10 years agoHelpfull: Yes(40) No(3)
• x^100=31 digit
  we know that,
  10^1=10
  10^2=100,means three digits
  10^3-1=3 digit
  10^31-1=x^100
  10^30=x^100
  30 log10=100 logx
  now,suppose that
  10^y-1=x^1000
  (y-1)log10=1000 logx
  y-1=10*100 logx
  y-1=300
  y=301
• 10 years agoHelpfull: Yes(7) No(4)
• 301 digits..
  for power 100 characterstic is 30
  so..for 1000 it will be 300..
  number of digits will be 301..
• 10 years agoHelpfull: Yes(4) No(1)
• Ans:- 302
  
  here X=2
  
  So,
  
  100log2 + 1= 31.103
  
  1000log2 +1= 302.03
• 10 years agoHelpfull: Yes(4) No(3)
• x^100=31 digit number
  X^1000 can be written as (X^100)^10
  which can again be converted to 10 log(x^100) = 10*31 = 310 digit number.
  so ans is 310.
• 10 years agoHelpfull: Yes(2) No(0)
• 302 digits
• 10 years agoHelpfull: Yes(1) No(1)
• Rakesh please solve this
• 10 years agoHelpfull: Yes(1) No(0)
• How @Moumita ??
• 10 years agoHelpfull: Yes(0) No(0)
• ans is 110
• 10 years agoHelpfull: Yes(0) No(1)
• 3 digit number lies between 10^2 to 10^3.Similarly,
  31 digit means the number lies between 10^30 to 10^31.
  (10^30)=< X^100 < 10^31 where =< represents less than or equal to.
  (10^30)^10 =< (X^100)^10 < (10^31)^10
  10^300 =< X^1000 < 10^310.-------(1)
  If a number lies between 10^2 to 10^3 then it has 3 digit(eg-777 lies between 10^2 to 10^3 and it has 3 digit).
  Similarly, eqn (1) will have 301 to 310 digits.
• 10 years agoHelpfull: Yes(0) No(1)
• 10^2=3 digit
  10^3=4 digit
  10^4=5 digit
  10^30=31 digit=x^100(as given in question)
  or, 10^31=x^100
  => log 10^31= log x^100(applying log)
  => 31 log 10=100 log x
  =>310 log 10= 1000 log x(multiply with 10 both side)
  => 10^310=x^1000
  now we know, 10^300= 301 digit
  so, x^1000= 301 digit
  
• 10 years agoHelpfull: Yes(0) No(0)