# Logarithms Quiz Set 008

### Question 1

Let us suppose that log(5) = 3, then what is log($1/50$) if the base is 10?

A

-4.

B

$\text"log"_3(50)$.

C

$\text"log"_5(30)$.

D

4.

Soln.
Ans: a

We know log($1/{10m}$) = log(1) - (log(10) + log(m)) = 0 - (1 + 3) = -4.

### Question 2

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.

### Question 3

What is the value of $\text"log"_2(√2)$?

A

$1/2$.

B

$2$.

C

$\text"log"_√2(2)$.

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 4

What is $1/{\text"log"_4(60)}$ + $1/{\text"log"_3(60)}$ + $1/{\text"log"_5(60)}$?

A

$1$.

B

5.

C

12.

D

0.

Soln.
Ans: a

The given expression simplifies to $\text"log"_60(4)$ + $\text"log"_60(3)$ + $\text"log"_60(5)$ = $\text"log"_60(4 × 3 × 5)$ = $\text"log"_60(60)$ = 1.

### Question 5

What is x if logx(y) = 4 and log2(x) = 3?

A

48.

B

$√8$.

C

$√{4/3}$.

D

$√{3/4}$.

Soln.
Ans: a

By definition, log2(x) = 3 gives x = 23 = 8. We are also given logx(y) = 4, which gives y = 4x = 48.