# Logarithms Quiz Set 011

### Question 1

Which of these is correct?

A

$\text"log"(1 + 2 + 3)$ = $\text"log"(1 × 2 × 3)$.

B

$\text"log"_8(8)$ = 8.

C

$\text"log"_4(4)$ = 16.

D

$\text"log"_3(1)$ = 3.

Soln.
Ans: a

Speaking factually, log(m + n + p) = log(m × n × p) is possible only if m × n × p = m + n + p, hence the answer, because 1 × 2 × 3 = 1 + 2 + 3. Expressions of the form $\text"log"_m(n) = p$ are same as mp = n. We can see that none of the other options makes it correct.

### Question 2

What is the value of $\text"log"_4(√4)$?

A

$1/2$.

B

$2$.

C

$\text"log"_√4(4)$.

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 3

Let us suppose that log(4) = 2, then what is log($1/40$) if the base is 10?

A

-3.

B

$\text"log"_2(40)$.

C

$\text"log"_4(20)$.

D

3.

Soln.
Ans: a

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

### Question 4

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 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. 