Arithmatical - Logarithms

DIRECTIONS : Problems based on Logs.
11. If log 2 = 0.30103, Find the number of digits in 256 is
  A.  17
  B.  19
  C.  23
  D.  25
Solution
Log( 256)=(56×0.30103)
= 16.85768.
Its characteristics is 16.
Hence, the number of digits in 256 is 17.
12. If ( log 5 5) (log 4 9) (log 3 2) is equal to
  A.  1
  B.  3/2
  C.  2
  D.  5
Solution
Given expression=log 9/log 4 ×log 2/log 3
‹=› log 3²/log 2²×log 2/log 3
= 2 log 3/ 2 log 2×log 2/log3
= 1.

13. If ax = by
  A.  log a/b = x/y
  B.  log a/ log b = x/y
  C.  log a/ log b = y/x
  D.  Non
Solution
ax = by = log ax= log by
‹=› x log a = y log b
‹=› log a / log b= y/x.
14. log√ 8 / log 8 is equal to
  A.  1/√8
  B.  1/4
  C.  1/2
  D.  1/8
Solution
log√ 8 / log 8= log(8)1/2 / log 8
= 1/ 2 log 8 /log 8
= 1/ 2.
15. If ( log b a) (log c b) (log a c) is equal to
  A.  0
  B.   1
  C.  abc
  D.  a+b+c
Solution
Given expression=(log a/log b×log b/log c ×log c/log a)
= 1.
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