# Logarithms Quiz Set 016

### Question 1

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

A

log($2/3$).

B

log($3/2$).

C

log2(3).

D

log3(2).

Soln.
Ans: a

log($m/n$) = log(m) - log(n) always.

### 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

Which of these is correct?

A

$\text"log"(1 + 2 + 3)$ = $\text"log"(1 × 2 × 3)$.

B

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

C

$\text"log"_6(6)$ = 36.

D

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

Soln.
Ans: a

Speaking factually, log(m + n + p) = log(m × n × p) is possible only if m × n × p = m + n + p, hence the answer, because 1 × 2 × 3 = 1 + 2 + 3. Expressions of the form $\text"log"_m(n) = p$ are same as mp = n. We can see that none of the other options makes it correct.

### 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

If log(343) = 3, what is log(49)?

A

2.

B

$\text"log"_49(7)$.

C

$\text"log"_7(343)$.

D

1/2.

Soln.
Ans: a

We have 3 = log343 = log$7^3$ = 3 log 7, which gives log7 = 1. So, 2 = 2 × log7 = log$7^2$ = log49. Hence, the answer is 2.