# Logarithms Quiz Set 019

### Question 1

What is the value of log2(4)?

A

2.

B

$√2$.

C

0.

D

$√4$.

Soln.
Ans: a

Let log2(4) = P. By definition, we have 2P = 4 = 22, which gives 2 as the answer.

### Question 2

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 3

Which of these is correct?

A

$\text"log"_7(7)$ = 1.

B

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

C

$\text"log"_3(3)$ = 9.

D

$\text"log"(7 + 2 + 3)$ = $\text"log"(42)$.

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

$\text"log"_2(2)$ = 1.

B

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

C

$\text"log"_3(3)$ = 9.

D

$\text"log"(2 + 5 + 3)$ = $\text"log"(30)$.

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 5

What is the value of log(3) + log(2)?

A

log($3 × 2$).

B

log($2 + 3$).

C

log3(2).

D

log2(3).

Soln.
Ans: a

log(mn) = log(m) + log(n) always.