# Logarithms Quiz Set 004

### Question 1

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.

### Question 2

Let us suppose that $\text"log"_3(4)$ = 4, then what is $\text"log"_4(3)$?

A

$1/4$.

B

$4$.

C

$\text"log"_4(√4)$.

D

5.

Soln.
Ans: a

From the theory of logarithms, we know that $\text"log"_4(3)$ = $1/{\text"log"_3(4)}$ = $1/4$.

### Question 3

Let us suppose that $\text"log"_6(2)$ = 2, then what is $\text"log"_2(6)$?

A

$1/2$.

B

$2$.

C

$\text"log"_2(√2)$.

D

3.

Soln.
Ans: a

From the theory of logarithms, we know that $\text"log"_2(6)$ = $1/{\text"log"_6(2)}$ = $1/2$.

### Question 4

Let us suppose that log(5) = 3, then what is log($1/50$) if the base is 10?

A

-4.

B

$\text"log"_3(50)$.

C

$\text"log"_5(30)$.

D

4.

Soln.
Ans: a

We know log($1/{10m}$) = log(1) - (log(10) + log(m)) = 0 - (1 + 3) = -4.

### Question 5

What is log$6/4$ + log$4/6$?

A

0.

B

$\text"log"_4(6)$.

C

$\text"log"_6(4)$.

D

1/2.

Soln.
Ans: a

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