# Logarithms Quiz Set 001

### Question 1

What is the value of $\text"log"_3(√3)$?

A

$1/2$.

B

$2$.

C

$\text"log"_√3(3)$.

D

0.

Soln.
Ans: a

From the theory of logarithms, we know that $\text"log"_m(√m)$ = $1/2$ × $\text"log"_m(m)$ = $1/2$ × 1 = 1/2.

### Question 2

What is P if $\text"log"_5(3)$ + $\text"log"_5(3P + 1)$ = 1 + $\text"log"_5(P + 3)$?

A

3.

B

4.

C

2.

D

2.

Soln.
Ans: a

We have $\text"log"_5(3)$ + $\text"log"_5(3P + 1)$ = $\text"log"_5(5)$ + $\text"log"_5(P + 3)$. It is same as $\text"log"_5(3 × (3P + 1))$ = $\text"log"_5(5 × (P + 3))$. Equating the logs, $3 × (3P + 1) = 5 × (P + 3)$, solving for P we get P = 3.

### Question 3

If log(216) = 3, what is log(36)?

A

2.

B

$\text"log"_36(6)$.

C

$\text"log"_6(216)$.

D

1/2.

Soln.
Ans: a

We have 3 = log216 = log$6^3$ = 3 log 6, which gives log6 = 1. So, 2 = 2 × log6 = log$6^2$ = log36. Hence, the answer is 2.

### Question 4

What is the value of log(5) - log(2)?

A

log($5/2$).

B

log($2/5$).

C

log5(2).

D

log2(5).

Soln.
Ans: a

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

### Question 5

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.