This document contains 15 problems related to logarithms and their properties. It includes the name of the author, their contact information, and the date. For each problem, the author has written the problem statement and solution. The problems cover topics like simplifying logarithmic expressions, determining unknown variables from logarithmic equations, and finding integral parts of logarithms.

1. LOGARITHMS
LEVEL 2
C.S.VEERARAGAVAN
98948 34264
veeraa1729@gmail.com

2. Simplify log(27)(16)(24)(18)
1) 4 2)2 3)1 4) 3
log(27)(16)(24)(18) = log(27)(16)(3x8)(9x2)
= log(27)(16)(27)(16)
= 1
12-Jun-15
C.S.VEERARAGAVAN 9894834264
veeraa1729@gmail.com 2
I

3. If logxa = logya , both x,y > a and
a is natural number then which of
the following is necessarily true?
1) x is always equal to y
2) x is never equal to y
3) x need not be equal to y
logxa = logya implies xt = yt = a
When t = 0, x need not be equal to y
When t = 1, x should be equal to y
When t = 2, x need not be equal to y.
In general x need not be equal to y.
12-Jun-15
C.S.VEERARAGAVAN 9894834264
veeraa1729@gmail.com 3
II

4. If log36 + log312 = log3m, m =
?
1) 9 2) 18 3) 3 4)
72
12-Jun-15
C.S.VEERARAGAVAN 9894834264
veeraa1729@gmail.com 4
III

5. Simplify log248 – log26.
1)log242
2) log254
3)log2288
4) log28
12-Jun-15
C.S.VEERARAGAVAN 9894834264
veeraa1729@gmail.com 5
IV

6. What is the value of log4m0
where m ≠ 0
1) 1 2) 2 3) 3 4) 0
12-Jun-15
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veeraa1729@gmail.com 6
V

7. Simplify: log482
1) 2 2) 3 3) 4 4) 6
12-Jun-15
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veeraa1729@gmail.com 7
VI

8. If log49 . logx2 = 1, x =?
1) 9 2)
1
9
3)
1
3
4)3
log49 . logx2 = 1
log 9
log 4
log2
log 𝑥
= 1
2log 3
2log 2
log2
log 𝑥
= 1
x = 3
12-Jun-15
C.S.VEERARAGAVAN 9894834264
veeraa1729@gmail.com 8
VII

9. 𝑙𝑜𝑔79
𝑙𝑜𝑔716
1) log32 2) log23
3) log43 4) log34
𝑙𝑜𝑔79
𝑙𝑜𝑔716
2𝑙𝑜𝑔73
2𝑙𝑜𝑔74
𝑙𝑜𝑔43
𝑙𝑜𝑔44
12-Jun-15
C.S.VEERARAGAVAN 9894834264
veeraa1729@gmail.com 9
VII
I

10. If 2𝑙𝑜𝑔232
= 𝑘, what is the value
of k?
1) 81 2) 27 3) 9 4)
243
2𝑙𝑜𝑔232
= 𝑘
Since 𝑎 𝑙𝑜𝑔 𝑎 𝑁
= N
12-Jun-15
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veeraa1729@gmail.com 10
IX

11. If 4 = log3p, p = ?
1) 81 2) 27 3) 9 4)
243
34 = p
12-Jun-15
C.S.VEERARAGAVAN 9894834264
veeraa1729@gmail.com 11
X

12. 𝑙𝑜𝑔916 =
𝑙𝑜𝑔94
𝑙𝑜𝑔 𝑥3
, 𝑡ℎ𝑒𝑛 𝑥 =?
1) 3 2) 9 3) 27 4)
81
𝑙𝑜𝑔916 =
𝑙𝑜𝑔16
𝑙𝑜𝑔9
2𝑙𝑜𝑔4
2𝑙𝑜𝑔3
𝑙𝑜𝑔94
𝑙𝑜𝑔93
12-Jun-15
C.S.VEERARAGAVAN 9894834264
veeraa1729@gmail.com 12
XI

13. If logax = logay , where a ≠ 1,
both x,y are positive then which
of the following is necessarily
true?
1) x is always equal to y
2) x is never equal to y
3) x need not be equal to y
12-Jun-15
C.S.VEERARAGAVAN 9894834264
veeraa1729@gmail.com 13
XII

14. If log169 = k log23, then k = ?
1) 1 2) 2 3)
1
2
4)
1
4
𝑙𝑜𝑔169 =
𝑙𝑜𝑔9
𝑙𝑜𝑔16
2𝑙𝑜𝑔3
2𝑙𝑜𝑔4
𝑙𝑜𝑔23
𝑙𝑜𝑔24
1
2
𝑙𝑜𝑔23
12-Jun-15
C.S.VEERARAGAVAN 9894834264
veeraa1729@gmail.com 14
XIII

15. What is the integral part of
log210000?
1) 11 2) 12 3) 13
4) 14
10000 lies between 213 and 214.
Hence log210000 lies between 13 & 14
12-Jun-15
C.S.VEERARAGAVAN 9894834264
veeraa1729@gmail.com 15
XIV

16. If N is a 20-digit number, what is
the integral part of log10N?
1) 118 2) 19 3) 120 4)
21
Any 20 digit number lies between 1019
and 1020.
12-Jun-15
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veeraa1729@gmail.com 16
XV