log -- logarithm function

• Usage:

  log x

  log(b,x)

  log_b x

  log I

  log(b,I)

  log_b I

  log(J,x)

  log_J x

  log(J,I)

  log_J I

• Inputs:
  • x, a real number or a complex number,
  • b, a real number, the base for the logarithm
  • I, a real interval or a complex interval,
  • J, a real interval, an interval of bases for the logarithm
• Outputs:
  • a real number or a complex number, the logarithm of x
  • a real interval or a complex interval, an interval containing the logarithms of all the points of I
  • a real number, a complex number, a real interval, or a complex interval, an interval containing the logarithms for bases in J

i1 : log 10

o1 = 2.302585092994046

o1 : RR (of precision 53)

i2 : log_2 10

o2 = 3.321928094887363

o2 : RR (of precision 53)

i3 : log_10 2p100

o3 = .3010299956639811952137388947246

o3 : RR (of precision 100)

i4 : log interval(2,3)

o4 = [.6931471805599453,1.09861228866811]

o4 : RRi (of precision 53)

i5 : log interval(1+2*ii,3+4*ii)

o5 = [.8047189526259899,1.609437916427851]+[.5880025904625654,
     1.325817666947842]*ii

o5 : CCi (of precision 53)