## Logarithm

#### Logarithm

1. If log 2 = 0.3010, then the number of digits in 264 is ?
1. 18
2. 19
3. 20
4. 21

1. Required answer = [64 log10 2] + 1

##### Correct Option: C

Required answer = [64 log10 2] + 1
= [ 64 x 0.3010 ] + 1
= 19.264 + 1
= 19 + 1
= 20

1. The value of $\frac{\log_{a}{x}}{\log_{ab}{x}} - \log_{a}{b}$ is ?
1. 0
2. 1
3. a
4. ab

1. ∵ loga x = ( logabx) / (logaba)
∴ The given expression = [[(logabx) / (logaba)] / [( logabx )] - ( logab)
= (1/logaba) - logab = logaab - logab = loga(ab/b)
= logaa = 1

##### Correct Option: B

∵ loga x = ( logabx) / (logaba)
∴ The given expression = [[(logabx) / (logaba)] / [( logabx )] - ( logab)
= (1/logaba) - logab = logaab - logab = loga(ab/b)
= logaa = 1

1. The value of log23 x log 32 x log34 x log43 is ?
1. 1
2. 2
3. 3
4. 4

1. Given Exp.= log23 x log 32 x log34 x log43
= (log3 / log2) x ( log2 / log3) x (log4 / log3) x (log3 / log4)

##### Correct Option: A

Given Exp.= log23 x log 32 x log34 x log43
= (log3 / log2) x ( log2 / log3) x (log4 / log3) x (log3 / log4) = 1

1. Given that log10 2 = 0.3010, then log2 10 is equal to ?
1. 0.3010
2. 0.6990
3. 1000 / 301
4. 699 / 301

1. log2 10 = log 10 / log 2
= 1 / log 2
= 1.0000 / 0.3010

##### Correct Option: C

log2 10 = log 10 / log 2
= 1 / log 2
= 1.0000 / 0.3010
= 1000 / 301

1. The value of log 9/8 - log 27/32 + log3/4 is ?
1. 0
2. 1
3. 2
4. 3

1. Given Exp. = log [{(9/8) / (27/32)} x 3/4)]
= log [(9/8) x (3/4) x (32/27)]
= log 1

##### Correct Option: A

Given Exp. = log [{(9/8) / (27/32)} x 3/4)]
= log [(9/8) x (3/4) x (32/27)]
= log 1
= 0