Quote:
Originally Posted by crack_2009
How many different prime numbers are factor of N if
log11log13log17log19N =23
where 11,13,17,19 are bases to log ?
options
1) 2
2) 7
3) 4
4) 0
5) None of these
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(loglogloglog N )/log11*log13*log*17*log19 = 23
log log log log N = 23 * log11 * log13 * log17 * log19
log log log log N = 23 * log(11+13+17+19)
log log log log N = 23 * log(60)
log log log N = 60^23
log log N = 10 ^ (60^23)
log N = 10 ^ (10^ 60 ^23)
N = 10 ^ (10 ^ 10 ^ 60 ^ 23)
N = (5 * 2) ^ (10 ^ 10 ^ 60 ^ 23)
Hence there should be 2 prime nos only.
2(Option 1)
Plz post the OA for this.