# Logarithms Quiz Set 013

### Question 1

What is $1/{\text"log"_6(48)}$ + $1/{\text"log"_2(48)}$ + $1/{\text"log"_4(48)}$?

A

$1$.

B

4.

C

12.

D

0.

Soln.
Ans: a

The given expression simplifies to $\text"log"_48(6)$ + $\text"log"_48(2)$ + $\text"log"_48(4)$ = $\text"log"_48(6 × 2 × 4)$ = $\text"log"_48(48)$ = 1.

### Question 2

Let us suppose that $\text"log"_3(4)$ = 4, then what is $\text"log"_4(3)$?

A

$1/4$.

B

$4$.

C

$\text"log"_4(√4)$.

D

5.

Soln.
Ans: a

From the theory of logarithms, we know that $\text"log"_4(3)$ = $1/{\text"log"_3(4)}$ = $1/4$.

### Question 3

Suppose for the sake of this question that $\text"log"_4(5)$ = 10. Then what is $\text"log"_5(1024)$?

A

1/2.

B

$\text"log"_4(5)$.

C

$\text"log"_5(4)$.

D

2.

Soln.
Ans: a

$\text"log"_5(1024)$ is same as $\text"log"_5(4^5)$ = 5 × $\text"log"_5(4)$ = $5/{\text"log"_4(5)}$, which is same as $5/10$ = 1/2.

### Question 4

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.

### Question 5

What is the value of log(4) + log(5)?

A

log($4 × 5$).

B

log($5 + 4$).

C

log4(5).

D

log5(4).

Soln.
Ans: a

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