Question 1

log -1/3 81 is equal to?

Accepted Answer

Let log-1/381 = x ⇒ 81 = (-1/3)x ⇒ 34 = (-1/3)x = 3-x ∴ x = -4

Question 2

If log 10 {log 10[log 10(log 10N )]} = 0, then the value of N is?

Accepted Answer

If log10{log10[log10(log10N)]} = 0 ⇒ log10{log10(log10N)} = 1 ⇒ log10(log10N) = 10 ⇒ log10N = 1010 ∴ N = 101010

Question 3

The value of 25 log 5 4 is?

Accepted Answer

Exp. = 25 log54 = 52 log54 = 5 log5 42 = 16

Question 4

The value of log 10 0.000001 is?

Accepted Answer

Exp. = log10 10-6 = -6

Question 5

The value of log 10 (0.00001) is?

Accepted Answer

Exp. = log10 10-5 = -5

Question 6

The value of log 6 log 5 15625 is?

Accepted Answer

log6 log515625 = log6 log5(5)6 = log66(log55) = 1

Question 7

If log 10000x = -1/4, then x is?

Accepted Answer

∵ log104x = -1/4 ⇒ x = (104)-1/4 = 1/10

Question 8

log x (16/25) = -1/2, then x is?

Accepted Answer

∵ logx(16/25) = -1/2 ⇒ 16/25 = (x)-1/2 = 1/x1/2 ∴ x = 625/256

Question 9

The value of log 2 (1/64) is?

Accepted Answer

log2(1/64) = log21 - log2 26 = 0 - 6 = -6

Question 10

If log a 3 = 1/3, then value of a is?

Accepted Answer

∵ loga3 = 1/3 ⇒ 3 = (a)1/3 ∴ a = 27

Question 11

If log 10 x = 7, then value of x is?

Accepted Answer

log10x = 7 ∴ x = 107

Question 12

If p x = q, then?

Accepted Answer

∵ px = q ⇒ logppx = logpq ⇒ xlogpp = logpq ∴ x = logpq (∵logpp = 1)

Question 13

Given that log 10 2 = 0.3010 the value of log 10 5 is?

Accepted Answer

log105 = log10(10/2) = log1010 - log102 = 1-0.3010 = 0.6990

Question 14

If log 10 (10x) = 2.7532, then log 10 (10000x) is?

Accepted Answer

log10(103.10x) = log10 103 + log10(10x) = 3 + 2.7532 = 5.7532

Question 15

If log 125 / log 5 = x, then x is equal to?

Accepted Answer

If log 125 / log 5 = x then x = 3log5 / log5= 3

Question 16

(log 5 3 ) x (log 3 625) is equal to?

Accepted Answer

(log53) x log3 54 = [log3 / log5] x 4 x [log5 / log3] = 4

Question 17

log 9 27 - log 27 9 is equal to?

Accepted Answer

Given Exp. = log927 - log279 = log27 / log9 - log9 / log27 = 3log3 / 2log3 - 2log3 / 3log3 = 3/2 - 2/3 = 5/6

Question 18

If 10 x = 1.73 and log 10 1730 = 3.2380, then x is equal to?

Accepted Answer

∵ 10x = 1730/1000 ∴ log10x= log101730 - log101000 ⇒ x = 3.2380 - 3 = 0.2380

Question 19

The value of log an / log abn is given by?

Accepted Answer

logan / logabn = [( log n / log a) / (log n / log (a.b))] = log (a.b) / log a = ( log a + log b) / log a = 1 + (log b / log a) = 1 + logab

Question 20

If A = log 27625 + 7log 1113 and B = log 9125 + 13log 107 then which of the following is true?

Accepted Answer

A = log27625 + 7log1113 = log3354 + 7 log1113 = 4/3 log3 5 + 7 log1113 B = log9125 + 13 log117 = log32 53 + 13 log117 = 3/2 log3 5 +13 log11 7 Let log3 5 = x and by the above rule 7 log11 13 = 13 log11 7 Therefore, A = 4/3 x + 13 log11 7 and B = 3/2 x + 13 log11 17 clearly, A < B hence (B) is the correct answer.

Logarithm Questions