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Properties of Logarithm
(i) log mn = log m + log n
(ii) log (m/n) = log m – log n
(iii) log mn = n log m
(iv) log a x log b = 1
(v) logb c x logc b = 1

1. If a, b, c are three consecutive integers, greater then zero, then log (l + ab) ÷ log b has the value
(a) –3 (b) 2 (c) 3 (d) –2
2. The value of log5 125 – log4 256 is
(a) 2 (b) 1 (c) 5 (d) 0
3. If logl02 = x and logl03 = y, then value oflogl0 1.2 is expressed in the terms of x and y as
(a) 2x + y – 1 (b) 1 + x + y (c) l – x + y (d) x - y + 1
4. If a, b, c are in G.P., then logax, logbx, logcx are in
(a) A.P. (b) G.P., (c) H.P. (d) None
5.. Log2[log2{log3(log3273)}] is equal to
(a) 1/2 (b) 1 (c) 2 (d) 0
6. alog b – log c x blog c – log a x clog a – log b has a value of
(a) 1 (b) 0 (c) – 1 (d) None
7. Log464 x log8190 x log25250 x log72925 x log10 12
(a) 1 (b) 1/2 (c) 0 (d) log81125
8. log (1 + 2 + 3) is exactly equals to
(a) log 1 + log 2 + log 3 (b) log (1 x 2 x 3) (c) Both (a) and (b) (d) None
9. If m = 10, then find log3(m3 – m2 – m + 1) – log3(m + 1) – log3(m – 1) is equal to
(a) 8 (b) 9 (c) 10 (d) 2
10. If log5 [log2 {log4 (y – 5)}] = 0, then y is equal to
(a) 21 (b) 31 (c) 17 (d) 16
11. If a2 . log3x = b . log27x, then
(a) a = 3 (b) 3a2 = b (c) b2 = 3a (d) None
12. [log22 + log24 + log28 + log216 + log232] is equal to
(a) 15 (b) log132768 (c) log262 (d) None
13. If log a, log b, log c are in A.P., then:
(a) a, b, c, are in G.P. (b) a2, b2, c2 are in G.P. (c) a, b, c, are in A.P. (d) a, b, c, are in H.P.
14. log [1 – {1 – (1 – x2)-1}-1]-1/2 can be written as
(a) log x2 (b) log 1/x (c) log x (d) None of these
15. If 2 log a + 3 log b – 2 = 0, the value of a2b3 is
(a) 104 (b) 10 (c) 102 (d) 103
16. The value of (logba) (logcb) (logac) is equal to:
(a) 100 (b) 1 (c) 10 (d) log (abc)
17. Find x, if logx 10 + logx 100 + logx 1000 = 6
(a) 10 (b) 2 (c) 4 (d) 6
18. If x2 + x – 1 = 0, then logcx + logc(1 + x) is equal to
(a) – 1 (b) 0 (c) 1 (d) 2