X=99^n.
i)Find the least value of n for which the 1st digit of X is 8.
ii)Find the least value of n for which the 1st digit of X is 7.

• 1)99^11=8.....
  2)99^23=7..
  so n=11 and 23.
• 11 years agoHelpfull: Yes(18) No(27)
• there are no such values of n because:
  99^2=9801
  99^3=970299
  99^4=96059601
  and so on..
• 11 years agoHelpfull: Yes(15) No(7)
• there is no value of x which will satisfy the eqn
  for both cases,
  NO SOLN
• 11 years agoHelpfull: Yes(11) No(4)
• X=99^n
  =(3*3*11)^n
  =3^2n*11^n
  soln 1) 11^n gives 1 as last digit for any value of n
  3^2n always gives 3,9,7,1 as last digit for all n
  there is no soln for 1st case
  2)11^n gives 1 as last digit for any value of n
  3^2n will give 7 as last digit for 2n=3(least value)
  so n=3/2 is the reqd answer
• 11 years agoHelpfull: Yes(7) No(19)
• 11,23.these two values has 8& 7
• 11 years agoHelpfull: Yes(1) No(1)
• i) least value of n for which the 1st digit of x is 8=2
  ii)least value of n for which the 1st digit of x is 7=3
• 11 years agoHelpfull: Yes(1) No(18)
• For the first one the answer is 11
  
  Secnd one answer will be 23.
• 11 years agoHelpfull: Yes(1) No(3)
• @ manoj how u put ^11 bcz 99^11 gives a big value...cant get it
• 11 years agoHelpfull: Yes(0) No(3)
• 23 & 11...how r u gtng dis manoj?ne shrt trick?
  
• 11 years agoHelpfull: Yes(0) No(1)
• No Soln For this question
• 10 years agoHelpfull: Yes(0) No(3)
• we get only 9 in the first digit..so none is the answer
• 10 years agoHelpfull: Yes(0) No(1)
• i got the answer her we go
  first of all "1st digit of X is not unit digit of X"
  for example say y=342170 so this number has 1 st digit as 3 and unit digit as 0
  i think you got the point
  now let's come the point
  99^n
  n=1 99 i.e 99^1
  n=2 9801 i.e 99^2
  n=3 970299 .....
  n=4 96059601
  n=5 9509900499 ..
  ....
  ....
  ......................
  n=1 99
  n=2 98
  n=3 97
  n=4 96
  and so on
  
  ..........
  n=11 89
  at 99^11 the answer of 99^11 is starting with 8
  so answer is 11
  as well as for 1st digit to be 7 is at 23
  from above explaination reader may think that 7 come at 99^21 only. but it wont come
  thank you
• 5 years agoHelpfull: Yes(0) No(0)