# Logarithms Quiz Set 007

### Question 1

Suppose for the sake of this question that $\text"log"_3(6)$ = 12. Then what is $\text"log"_6(729)$?

A

1/2.

B

$\text"log"_3(6)$.

C

$\text"log"_6(3)$.

D

2.

Soln.
Ans: a

$\text"log"_6(729)$ is same as $\text"log"_6(3^6)$ = 6 × $\text"log"_6(3)$ = $6/{\text"log"_3(6)}$, which is same as $6/12$ = 1/2.

### Question 2

What is log$7$ + log$1/7$?

A

0.

B

$\text"log"_3(7)$.

C

$\text"log"_7(3)$.

D

1/2.

Soln.
Ans: a

log(m) + log(1/m) = log (m × $1/m$) = log 1 = 0.

### Question 3

What is the value of log(2) - log(1)?

A

log($2/1$).

B

log($1/2$).

C

log2(1).

D

log1(2).

Soln.
Ans: a

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

### Question 4

What is x if logx$(6/7)$ = 1?

A

${6/7}$.

B

${36/49}$.

C

$√{6/7}$.

D

$√{7/6}$.

Soln.
Ans: a

logx$(6/7)$ = 1, by definition, gives $x^1$ = $6/7$. So x = ${6/7}$.

### Question 5

Let us suppose that log(3) = 4, then what is log($1/30$) if the base is 10?

A

-5.

B

$\text"log"_4(30)$.

C

$\text"log"_3(40)$.

D

5.

Soln.
Ans: a

We know log($1/{10m}$) = log(1) - (log(10) + log(m)) = 0 - (1 + 4) = -5. 