# Logarithms Quiz Set 006

### Question 1

What is x if logx$(4/7)$ = 1?

A

${4/7}$.

B

${16/49}$.

C

$√{4/7}$.

D

$√{7/4}$.

Soln.
Ans: a

logx$(4/7)$ = 1, by definition, gives $x^1$ = $4/7$. So x = ${4/7}$.

### Question 2

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.

### Question 3

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 4

Let us suppose that log(7) = 2, then what is log($1/70$) if the base is 10?

A

-3.

B

$\text"log"_2(70)$.

C

$\text"log"_7(20)$.

D

3.

Soln.
Ans: a

We know log($1/{10m}$) = log(1) - (log(10) + log(m)) = 0 - (1 + 2) = -3.

### Question 5

What is $1/{\text"log"_7(210)}$ + $1/{\text"log"_6(210)}$ + $1/{\text"log"_5(210)}$?

A

$1$.

B

5.

C

18.

D

0.

Soln.
Ans: a

The given expression simplifies to $\text"log"_210(7)$ + $\text"log"_210(6)$ + $\text"log"_210(5)$ = $\text"log"_210(7 × 6 × 5)$ = $\text"log"_210(210)$ = 1.