# Logarithms Quiz Set 002

### Question 1

Which of these is correct?

A

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

B

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

C

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

D

$\text"log"(3 + 2 + 4)$ = $\text"log"(24)$.

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

What is ${\text"log"(√6)}/{\text"log"(6)}$?

A

1/2.

B

$\text"log"_6(√6)$.

C

$\text"log"_√6(6)$.

D

2.

Soln.
Ans: a

${\text"log"(√6)}/{\text"log"(6)}$ is same as ${\text"log"(6^{1/2})}/{\text"log"(6)}$, which is same as (1/2) × ${\text"log"(6)}/{\text"log"(6)}$ = 1/2.

### Question 3

What is the value of log2(16)?

A

4.

B

$√4$.

C

0.

D

$√16$.

Soln.
Ans: a

Let log2(16) = P. By definition, we have 2P = 16 = 24, which gives 4 as the answer.

### Question 4

What is P if $\text"log"_3(4)$ + $\text"log"_3(4P + 1)$ = 1 + $\text"log"_3(P + 4)$?

A

${8/13}$.

B

$1{3/4}$.

C

$2{4/15}$.

D

$3{2/15}$.

Soln.
Ans: a

We have $\text"log"_3(4)$ + $\text"log"_3(4P + 1)$ = $\text"log"_3(3)$ + $\text"log"_3(P + 4)$. It is same as $\text"log"_3(4 × (4P + 1))$ = $\text"log"_3(3 × (P + 4))$. Equating the logs, $4 × (4P + 1) = 3 × (P + 4)$, solving for P we get P = ${8/13}$.

### Question 5

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.