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21. Find the value of log55{log525 + log5125}.
  A.  5
  B.  2
  C.  3
  D.  1
     
   
View Answer

Shortcut:
logabn = nlogab
Note 1: loga(b)(1/n) =
1 / n
logab
Note 2: loga(b)−n = − nlogab
Here; log55{log525 + log5125}
or, log55{log5(25 x 125)
= log552 = 2log55 = 2

22. Find the value of log10(0.0001).
  A.  -4
  B.  -1
  C.  3
  D.  -2
     
   
View Answer

Shortcut:
logabn = nlogab
Note 1: loga(b)(1/n) =
1 / n
logab
Note 2: loga(b)−n = − nlogab
Here; log10(0.0001)
or, log1010−4
= 4log1010
= −4

23. Find the value of [log10(5log10100)]2
  A.  4
  B.  2
  C.  3
  D.  1
     
   
View Answer

Shortcut:
logabn = nlogab
Note 1: loga(b)(1/n) =
1 / n
logab
Note 2: loga(b)−n = − nlogab
Here; [log10(5log10100)]2
or, [log10(5log10102)]2
= [log10(10)]2 = 12 = 1

24. If log8 = 0.9031 and log9 = 0.9542, then find the value of log6.
  A.  0.7762
  B.  0.7684
  C.  0.7781
  D.  0.7790
     
   
View Answer

Shortcut:
logabn = nlogab
Note 1: loga(b)(1/n) =
1 / n
logab
Note 2: loga(b)−n = − nlogab
Here; log8 = log(2)3 = 3log2
or, 3log2 = 0.9031
∴ log2 =
0.9031 / 3
= 0.3010
Now, log9 = log(3)2 = 2log3
∴ 2log3 = 0.9542
⇒ log3 =
0.9542 / 2
= 0.4771
Now, log6 = log(2 x 3) = log2 + log3
= .3010 + 0.4771 = 0.7781

25. If log10m = b − log10n, then find the value of m.
  A.  
102b / n
  B.  
10b / n
  C.  
10b / 2n
  D.  
10b / 10n
     
   
View Answer

Shortcut:
log(ab) = log(a) + log(b)
Here; log10m = b − log10n
or, log10m + log10n = b
⇒ log10(mn) = b
⇒ 10b = mn
∴ m =
10b / n

26. If log2 = x, log 3 = y and log7 = z, then the value of log(4 × ∛63) is:
  A.  3x +
1 / 3
y +
2 / 2
z
  B.  5x +
2 / 3
y +
1 / 2
z
  C.  2x +
2 / 3
y +
1 / 3
z
  D.  3x +
3 / 2
y +
1 / 2
z
     
   
View Answer

Shortcut:
log(ab) = log(a) + log(b)
Here; log(4 × ∛63)
or, log
[
22 x (3 x 3 x 7)1/3
]

= log(2)2 + log(3 x 3 x 7)1/3
= 2log2 +
1 / 3
log(32 x 7)
= 2log2 +
1 / 3
log(3)2 + log7)]
= 2log2 +
2 / 3
log3 +
1 / 3
log7
= 2x +
2 / 3
y +
1 / 3
z

27. If log(0.57) =
/ 1
.756, then the value of log57 + log(0.57)3 + log√0.57 is:
  A.  0.960
  B.  0.885
  C.  0.982
  D.  0.902
     
   
View Answer

Shortcut:
log(ab) = log(a) + log(b)
Here; log57 + log(0.57)3 + log√0.57
or,log
57x100 / 100
+ 3log(0.57)+
1 / 2
log(0.57)
= log(0.57) +log102 + 3log(0.57)+
1 / 2
log(0.57)
=
(
1 + 3 +
1 / 2
)
log(0.57) + 2 [∵ log2 = 2]
= (4.5 x
/ 1
.756) + 2
= 4.5(−1 + 0.756) + 2
= 0.902

28. If log90 = 1.9542 then log3 equals to
  A.  0.4779
  B.  0.4771
  C.  0.4671
  D.  0.4873
     
   
View Answer

Shortcut:
log(ab) = log(a) + log(b)
Here; log90 = 1.9542
or, log(32 x 10) = 1.9542
or, 2log3 + log10 = 1.9542
or, log3 =
0.9542 / 2
= 0.4771

29. Find the value of
1 / 2
log25 − 2log103 + log1018, find the value of x.
  A.  1
  B.  5
  C.  3
  D.  2
     
   
View Answer

Shortcut:
log(ab) = log(a) + log(b)
Here;
1 / 2
log25 − 2log103 + log1018
or, log10(25)1/2 −log10(3)2 + log1018
or, log105 − log109 + log1018
or, log10
(
5 x 18 / 9
)
= log1010 = 1

30. Find the value of logx + log
(
1 / x
)
.
  A.  5
  B.  2
  C.  0
  D.  1
     
   
View Answer

Shortcut:
log(ab) = log(a) + log(b)
Here; logx + log
(
1 / x
)

or, logx + log1 − logx
or, logx + 0 − logx = 0

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