# 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

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.

### Question 3

What is x if logx$(3/5)$ = $1/2$?

A

${9/25}$.

B

${3/5}$.

C

$√{3/5}$.

D

$√{5/3}$.

Soln.
Ans: a

logx$(3/5)$ = $1/2$, by definition, gives $x^{1/2}$ = $3/5$. So x = $(3/5)^2$ = ${9/25}$.

### Question 4

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 5

What is the value of log(5) + log(6)?

A

log($5 × 6$).

B

log($6 + 5$).

C

log5(6).

D

log6(5).

Soln.
Ans: a

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