Logarithm Questions and Answers

Q1 :

If log $Big(frac{a + b}{3}Big) = frac{1}{2} left(text{log } a + text{log } b right)$

A

$a^2 + b^2 = ab$

B

$a^2 + b^2 = 7ab$

C

$a^2 + b^2 = -3ab$

D

$a^2 + b^2 = 3ab$

Right Answer: B

$a^2 + b^2 = 7ab$

Q2 :

The expression $text{ log } frac{11}{5} + text{log} frac{14}{3} - text{log } frac{22}{15 }$ is equal to

A

log 2

B

log 3

C

log 5

D

log 7

Q3 :

If $text{ log}_b a times text{ log}_y x = text{ log }_c a$ , then the value of $x$ and $y$ are respectively

A

$b text{ and } c$

B

$c text{ and } b$

C

$c text{ and } a$

D

$b text{ and } a$

Right Answer: A

$b text{ and } c$

Q4 :

If $log_{10} 7 = a$ , then $log_{10}Big(frac{1}{70}Big)$ is equal to

A

$frac{a}{10}$

B

$frac{1}{10a}$

C

$(1 + a)^{-1}$

D

$-(1 + a)$

Right Answer: D

$-(1 + a)$

Q5 :

If antilog (0.0385) = 1092 and $log x = bar 3.0385$ , then $x$ is equal to

A

.1092

B

.01092

C

.001092

D

.0001092

Q6 :

The value of, $frac{1}{3} log_{10} 125 - 2 log_{10} 4 + log_{10} 32$ is

A

0

B

1

C

2

D

3

Q7 :

For 0 < a <1, the numbers $frac{1}{a}$ , $a, a^2 log$ a when arranged in ascending order of their values, are:

A

$log a, a^2, a, frac{1}{a}$

B

$a, frac{1}{a}, log a, a^2$

C

$a, a^2, log a, frac{1}{a}$

D

$log a, frac{1}{a}, a, a^2$

Right Answer: A

$log a, a^2, a, frac{1}{a}$

Q8 :

The value of $log_{10} 125$ , (given $log_{10} 2 = 0.30$ ), is

A

2.05

B

2.10

C

2.15

D

2.21

Q9 :

What is the value of log $_{100}$ 0.1 ?

A

1/2

B

-1/2

C

-2

D

2

Q10 :

The value of 3 log 3 + 2 log 2 is

A

log 108

B

log 106

C

log 109

D

None of these

Q11 :

If log $_2$ $sqrt{2} = frac{1}{6}$ , then the value of $a$ is

A

$(sqrt{2})^6$

B

$(6)^{frac{1}{2}}$

C

3

D

-6

Right Answer: A

$(sqrt{2})^6$

Q12 :

Find the logarithm of 1728 to the base $2sqrt{3}$

A

3.124

B

3.1732

C

6

D

5

Q13 :

What is the value of $frac{1}{2}$ log $_{10}$ 25 - 2log $_{10}$ 3 + log $_{10}$ 18 ?

A

2

B

3

C

1

D

0

Q14 :

What is the value of $[text{log}_{10} hspace{0.2cm} (5 text{ log}_{10} hspace{0.2cm}100)]^2$ ?

A

4

B

3

C

2

D

1

Q15 :

The value of $text{log}_y hspace{0.2cm} x cdot text{log}_z hspace{0.2cm} y cdot text{log}_x hspace{0.2cm} z$ is

A

log xyz

B

xyz

C

1

D

0