Arithmatical - Logarithms

DIRECTIONS : Problems based on Logs.
6. The value of log2(log5625) is
  A.  2
  B.  5
  C.  10
  D.  15
Solution
Let log5625= x.
Then, 5x= 625
= 54
‹=› x=4.
Let log2( log5625)= y.
Then, log 24= y
‹=› 2y= 4
y;2.
7. The value of log5(1/ 125) is
  A.  3
  B.  -3
  C.  1/3
  D.  -1/3
Solution
Let log5(1/125)= n.
Then, 5n= 1/125
‹=›5n =5-3
n= -3.

8. If logx y =100 and log2 x =10, then the values of y is
  A.  210
  B.  2100
  C.  21000
  D.  210000
Solution
log2 x= 10
x= 210
logx y= 100
y= x100
=(210)100
y‹=›21000
9. Evaluate :log3 27
  A.  3
  B.  4
  C.  5
  D.  6
Solution
log3 27= n
=3n
=27
=33
n‹=›3.
10. If log√8 x = 3×1/3, find the value of x.
  A.  25
  B.  32
  C.  37
  D.  None of these
s
Solution
log√8 x = 10/3.
x =( 8)10/3
=2( 3/2×10/3)
=2 5
= 32.
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