Q. What is the probability log2(M)+log4(M) is integar where M is two digit integer and 2,4 are base.

• log2(M)+log4(M) ,,, since M is a 2-digit no... thus total outcomes for the solution is 90 wen we put the value of M from 10 to 99 thus giving each value... Now the value of equation is integer for only two two value i.e. 16 and 64 ,,,, as log2(16)+log4(16)= log2((2)^4)+log4((4)^2) = 4*1+2*1 = 6 .... as loge(e) is 1 same for the value of 64,,,, log2((2)^6)+log4((4)^3)) = 6+3=9 i.e. integer thus for the values of M we are getting only two values as integersss thus probability is 2/90=1/45
• 11 years agoHelpfull: Yes(60) No(2)
• Total outcome = 90
  Since log2(M)+log4(M)can be written as 2log2(M).
  Hence Sample value = {16, 32, 64}
  Prob = 3/90 = 1/30 ans.
• 11 years agoHelpfull: Yes(6) No(21)
• ooooppps 32 cant be the possible value
• 11 years agoHelpfull: Yes(6) No(1)
• @Kunal .... 32 can be the possible value as 32 is none of the powers of the 4 thus not giving integer value
• 11 years agoHelpfull: Yes(2) No(1)
• got it priyansh...
  sorry for the wrong ans.
  Correct ans - 1/45
• 11 years agoHelpfull: Yes(1) No(4)
• no of out comes=90;
  m value should be two digit and the output should be integer then only 16 and 64 is possible
  so the probability=2/90=1/45
  
• 10 years agoHelpfull: Yes(1) No(1)
• nw log2(M)+log4(M)
  =log2(M)+log2^2(M)
  =log2(M)+1/2log2(M){propty of log}
  =log2(M^3/2)nw 4^2 nd 8^2 gives integer value
  so,n(E)=2
  n(s)=9*10{as M is two digit no}
  soP(E)=n(E)/n(s)
  =2/90
  =1/45
• 10 years agoHelpfull: Yes(1) No(0)
• ans will be 1/30,
  bcoz we have total outcomes 90 and sample space will be {4,16,64}
• 10 years agoHelpfull: Yes(0) No(4)