# Logarithms Quiz Set 003

### Question 1

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 2

What is the value of log(3) + log(7)?

A

log($3 × 7$).

B

log($7 + 3$).

C

log3(7).

D

log7(3).

Soln.
Ans: a

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

### Question 3

What is x if logx(y) = 7 and log2(x) = 2?

A

74.

B

$√4$.

C

$√{7/2}$.

D

$√{2/7}$.

Soln.
Ans: a

By definition, log2(x) = 2 gives x = 22 = 4. We are also given logx(y) = 7, which gives y = 7x = 74.

### Question 4

What is ${\text"log"(√4)}/{\text"log"(4)}$?

A

1/2.

B

$\text"log"_4(√4)$.

C

$\text"log"_√4(4)$.

D

2.

Soln.
Ans: a

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

### Question 5

Which of these is correct?

A

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

B

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

C

$\text"log"_8(8)$ = 64.

D

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

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.