2^150 has total numbers???

Option
a)45
b)46
c)47
d)48

• let z=2^150
  log z= 150 log2
  log z=150*0.3010(log2=.3010)
  log y=45.15
  so, required no.is 46 ans.
• 11 years agoHelpfull: Yes(46) No(1)
• since 2^10 = 1024= 1.024*10^3(i.e 4 digits)
  
  hence 2^150 = (2^10)^15=(1.024*10^3)^15=1.024^15*10^45=1.36*10^45(i.e. 46 digits)
  
  
• 11 years agoHelpfull: Yes(12) No(1)
• above expression can be written as 32^30
  now,32^1 =32 has 2 digits
  32^2=1024 has 4 digits
  32^3 =32768 has 5 digits
  32^30 has 46 numbers
  
• 11 years agoHelpfull: Yes(10) No(13)
• 2^4 = 2 digits
  2^7 = 3 digits
  2^10 = 4 digits
  2^14 = 5 digits
  2^17 = 6 digits
  2^20 = 7 digits
  So there is increase of 3 in number of digits after every 10 powers so for 150/10 = 15 and every 10 has 3 digits of increase, so for 150 there will be 45 digits.
• 11 years agoHelpfull: Yes(6) No(4)
• let y=2^150
  log y= 150log2
  log y=150*.301
  log y=45.15
  then required no. = 46
• 11 years agoHelpfull: Yes(3) No(1)
• let y=2^150
  log y= 150log2
  log y=150*.301
  log y=45.15
  then required no. = 46
• 11 years agoHelpfull: Yes(1) No(0)
• topic:logarithm
  log(2^150)
  150log2=(150*0.3010) =45.15
  its characteristic is 45 hence the number of digits will be 46
• 10 years agoHelpfull: Yes(1) No(0)