Question 1

The simplified form of log(75/16) -2 log(5/9) +log(32/343) is?

Accepted Answer

Given Exp. = log75/16 - 2 log5/9 + log32/343 = log [(25 x 3) / (4 x 4)] - log (25/81) + log [(16 x 2) / (81 x 3)] = log(25 x 3) - log ( 4 x 4 ) - log(25) + log81 + log(16 x 2) -log (81 x 3) = log 25 + log 3 - log 16 - log 25 + log 81 + log 16 + log 2 - log 81 - log 3 = log 2

Question 2

If log 2 = 0.3010 then log 5 equals to?

Accepted Answer

log 5 = log 10 /2 = log 10 - log 2 = 1 - 0.3010 = 0.6990

Question 3

If log 102 =0.3010 and log 107 = 0.8451, then the value of log 10 2.8 is?

Accepted Answer

log102.8 = log10(28/10) = log 28 - log 10 = log (7 x 4 ) - log 10 = log 7 + 2 log 2 - log 10 = 0.8451 + 2 x 0.3010 - 1 = 0.8451 + 0.6020 - 1 = 0.4471

Question 4

If log 10 2 =0.301, then the value of log 10(50) is?

Accepted Answer

log1050 = log10[(50 x 2) / 2] = log 100 - log 2 = log10102 - log 2 = 2 - 0.301 = 1.699

Question 5

Find the value of log (a 2 / bc) + log (b 2 / ac) + log (c 2 / ab)?

Accepted Answer

Given Exp. = log (a2 / bc) + log (b2 / ac) + log (c2 / ab) = log [(a2 x b2 x c2) / (a2 x b2 x c2)] =log 1 =0

Question 6

Find the value of log 8 + log 1/8?

Accepted Answer

Given expression = log 8 + log (1/8) = log 8 x (1/8) = log 1 = 0

Question 7

The equation log ax + log a (1+x)=0 can be written as?

Accepted Answer

logax + loga(1+x) = 0 ⇒ logax (x+1) = loga1 (since log 1 = 0) ⇒ x(x +1) = 1 ∴ x2 + x - 1 = 0

Question 8

Find the value of log x + log (1/x)?

Accepted Answer

Given expression = log x + log1/x = log x + log 1 - log x = log 1 = 0

Question 9

If log 90 = 1.9542 then log 3 equals to?

Accepted Answer

Given log90 = 1.9542 ⇒ log(32 x 10) = 1.9542 ⇒ 2log 3 + log 10 = 1.9542 ∴ log 3 = 0.9542 / 2 = 0.4771

Question 10

If 2log 4x = 1 + log 4 (x-1), find the value of x.?

Accepted Answer

∵ 2log4x = 1 + log4(x-1) ⇒ log4x2 = log44 + log4(x-1) ⇒ x2 = 4(x-1) ⇒ x2 - 4x + 4 = 0 ⇒ (x-2)2 = 0 ∴ x = 2

Question 11

If log 3 = 0.477 and (1000) x = 3, then x equals to?

Accepted Answer

∵ (1000)x = 3 ⇒ xlog 103 = log 3 ⇒ 3x = log 3 ∴ x = log 3 / 3 = 0.477 / 3 = 0.159

Question 12

If 5 5-x = 2 x-5, find the value of x .?

Accepted Answer

∵ 55-x = 2x-5 ⇒ 55-x = 2-(5-x) ⇒ (5-x)log 5 = -(5-x)log 2 ⇒ (5-x)log 5 + (5-x)log 2 = 0 ⇒ (5-x){log 5 + log 2 } = 0 ⇒ (5-x){log10/2 + log 2 } = 0 ⇒ (5-x){log10 - log 2 + log 2} = 0 ⇒ 5-x = 0 ∴ x = 5

Question 13

If log 8 x + log 4 x + log 2x =11, then the value of x is?

Accepted Answer

∵ log23 x1 +log22 x1 + log2x = 11 ⇒ 1/3log2x + 1/2log2x + log2x = 11 ⇒ (1/3 + 1/2 +1)log2x = 11 ⇒ 11/6log2x = 11 ⇒ log2x = 11 x 6 / 11 =6 ∴ x = 26 = 64

Question 14

If 10 0.3010 = 2, then find the value of log 0.125 125.?

Accepted Answer

Exp. = log0.125125 = log2-3 53 = - 3/3log25 = -log25 ∵ 100.3010 = 2 ⇒ log102 = 0.3010 ∵ log105 = log1010/2 = log1010-log102 = 1-0.3010 = 0.6990 ∴ -log25 = - log105 / log102 = - 0.6990 / 0.3010 = - 699/301

Question 15

Find the value of log 0.125 64?

Accepted Answer

Exp. = log0.12564 = log2-3 26 ={6 / (-3)} log22 = -2

Question 16

Find the value of log 322 8 + log 2433 7 - log 361296?

Accepted Answer

Exp. =log3228 + log24337 - log361296 = log25 28 + log35 37 - log36 362 = (8/5)log22 + (7/5)log33 - 2log3636 = 8/5 + 7/5 - 2 = 1

Question 17

Find the value of log 49 16807 - log 9 27?

Accepted Answer

Exp. = log4916807 - log927 = log72 75 - log32 33 =(5/2)log77 - (3/2)log33 =5/2 - 3/2 = 1

Question 18

Find the value of log 9 81 - log 4 32?

Accepted Answer

log9 81 - log4 32 = log32 34 - log22 25 = 4/2 - 5/2 = -1/2

Question 19

log 1010 + log 10100 + log 101000 + log 1010000 + log 10100000 is equal to?

Accepted Answer

Given Exp. = log1010 + log10100 + log101000 + log1010000 + log10100000 = 1 + 2 + 3 + 4 + 5 = 15

Question 20

log 10x + log 10y = z, then x is equal to?

Accepted Answer

log10xy = z ⇒ xy = 10z ⇒ x = 10z/y

Logarithm Questions