# Logarithms Quiz Set 012

### Question 1

What is the value of $\text"log"_3(√3)$?

A

$1/2$.

B

$2$.

C

$\text"log"_√3(3)$.

D

0.

Soln.
Ans: a

From the theory of logarithms, we know that $\text"log"_m(√m)$ = $1/2$ × $\text"log"_m(m)$ = $1/2$ × 1 = 1/2.

### Question 2

What is log$4$ + log$1/4$?

A

0.

B

$\text"log"_3(4)$.

C

$\text"log"_4(3)$.

D

1/2.

Soln.
Ans: a

log(m) + log(1/m) = log (m × $1/m$) = log 1 = 0.

### Question 3

Which of these is correct?

A

$\text"log"_8(8)$ = 1.

B

$\text"log"_5(5)$ = 5.

C

$\text"log"_7(7)$ = 49.

D

$\text"log"(8 + 5 + 7)$ = $\text"log"(280)$.

Soln.
Ans: a

Expressions of the form $\text"log"_m(n) = p$ are same as mp = n. We can see that if m = n, then p = 1 will make it correct. Also, log(m + n + p) = log(m × n × p) is possible only if m × n × p = m + n + p.

### Question 4

Which of these is correct?

A

$\text"log"_6(2)$ = $1/{\text"log"_2(6)}$.

B

$\text"log"_2(2)$ = 2.

C

$\text"log"_4(4)$ = 16.

D

$\text"log"(6 + 2 + 4)$ = $\text"log"(48)$.

Soln.
Ans: a

Speaking factually, $\text"log"_m(n)$ = $1/{\text"log"_n(m)}$, hence the answer. Expressions of the form $\text"log"_m(n) = p$ are same as mp = n. We can see that none of the options makes it correct. Also, log(m + n + p) = log(m × n × p) is possible only if m × n × p = m + n + p.

### Question 5

Which of these is correct?

A

$\text"log"_3(3)$ = 1.

B

$\text"log"_6(6)$ = 6.

C

$\text"log"_2(2)$ = 4.

D

$\text"log"(3 + 6 + 2)$ = $\text"log"(36)$.

Soln.
Ans: a

Expressions of the form $\text"log"_m(n) = p$ are same as mp = n. We can see that if m = n, then p = 1 will make it correct. Also, log(m + n + p) = log(m × n × p) is possible only if m × n × p = m + n + p.