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Welcome to ICOME Quiz corner

Q1. The value of log(xn/ym) + log(yn/zn) + log(zn/xn).

(a) 1 (b) 2 (c) 3 (d) 0

Solution.
∴ log1 = 0
Solution

Q2. The value of the expression :alogax . logxy . logyz . logzb

(a) a (b) b (c) c (d) d

Solution.
alogab = b

∴ logax . logxy . logyz . logzb = logab

NOTE : alogak = k
Solution

Q3. log8(log5x) = 1/3, find x.

(a) 15 (b) 26 (c) 25 (d) 10

Solution.
log8(log5x) = 1/3log88

log8(log5x) = log881/3

log8(log5x) = log82

log5x = 2log55

log5x = log552

x = 25
Solution

Q4. Find the value of
log38/log916 . log410


(a) 3 log102 (b) log10 (c) 5logx (d) 10log4

Solution.
=
log 8/log 3
.
log 9/log 16
.
log 4/log 10
=
3 log 2 . 2 log 3 . 2 log 2/log3 . 4 log 2 . log 10


=
3log2/log 10


= 3 log102
Solution

Q5. If log 2 = 0.30103 , the number of digits in 216 is :

(a) 2 (b) 3 (c) 4 (d) 5

Solution.
(d) 5

x = 216

log x = 16 log 2 = 16 x (0.30103) = 4.81648

As characteristics of logx is 4, so x must have 5 digits.
Solution

Q6. (log a)2 - (log b)2 = ?

(a) log ab (b) log(a+b) (c) log(a/b) (d) log(ab). log(a/b)

Solution.
= (log a - log b).(log a + log b)

= log(ab). log(a/b)
Solution

Q7.
log97/log617
-
log37/log√617
= x , find x .

(a) 0 (b) 1 (c) 2 (d) 3

Solution.
log37/log617
-
log37/log617
= 0

{log97 =
log 7/log 9
=
log 7/2log 3
=
1/2
log37 =
log37/2
}
Solution

Q8. Find a2 + b2 if log(a+b)/5 = 1/2 (log a + log b)

(a) 15 (b) 15 ab (c) 23 (d) 23 ab

Solution.
log[(a+b)/5]2 = log(ab)

a2 + b2 + 2ab = 25ab

a2 + b2 = 23 ab
Solution

Q9. 4log a + 4log a2 + 4log a3 + --------- + 4log an = x, find x .

(a) 2n(n+1)log a (b) log a (c) 2n (d) (n+1)log a

Solution.
= 4[log a + log a2 + log a3 + --------- + log an]

= 4[log a(1 + 2 + 3 + ------+ n)]

= 4[log an(n+1)/2]

= 4
n(n+1)/2
log a

2n(n+1) log a
Solution

Q10. log√(27+10√2) = log(5+x), find x.

(a) 4 (b) 1 (c) √2 (d) √3

Solution.
log√[5 + √2]2 = log(5 + x)

5 + √2 = 5 + x

x = √2
Solution