# Logarithms Quiz Set 018

### Question 1

Suppose for the sake of this question that $\text"log"_3(2)$ = 4. Then what is $\text"log"_2(9)$?

A

1/2.

B

$\text"log"_3(2)$.

C

$\text"log"_2(3)$.

D

2.

Soln.
Ans: a

$\text"log"_2(9)$ is same as $\text"log"_2(3^2)$ = 2 × $\text"log"_2(3)$ = $2/{\text"log"_3(2)}$, which is same as $2/4$ = 1/2.

### 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

What is $1/{\text"log"_3(60)}$ + $1/{\text"log"_4(60)}$ + $1/{\text"log"_5(60)}$?

A

$1$.

B

5.

C

12.

D

0.

Soln.
Ans: a

The given expression simplifies to $\text"log"_60(3)$ + $\text"log"_60(4)$ + $\text"log"_60(5)$ = $\text"log"_60(3 × 4 × 5)$ = $\text"log"_60(60)$ = 1.

### 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

Suppose for the sake of this question that $\text"log"_2(7)$ = 14. Then what is $\text"log"_7(128)$?

A

1/2.

B

$\text"log"_2(7)$.

C

$\text"log"_7(2)$.

D

2.

Soln.
Ans: a

$\text"log"_7(128)$ is same as $\text"log"_7(2^7)$ = 7 × $\text"log"_7(2)$ = $7/{\text"log"_2(7)}$, which is same as $7/14$ = 1/2. 