# Logarithms Quiz Set 010

### Question 1

What is the value of log(6) + log(7)?

A

log($6 × 7$).

B

log($7 + 6$).

C

log6(7).

D

log7(6).

Soln.
Ans: a

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

### Question 2

Which of these is correct?

A

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

B

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

C

$\text"log"_6(6)$ = 36.

D

$\text"log"_8(1)$ = 8.

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 3

Let us suppose that $\text"log"_7(2)$ = 2, then what is $\text"log"_2(7)$?

A

$1/2$.

B

$2$.

C

$\text"log"_2(√2)$.

D

3.

Soln.
Ans: a

From the theory of logarithms, we know that $\text"log"_2(7)$ = $1/{\text"log"_7(2)}$ = $1/2$.

### Question 4

Which of these is correct?

A

$\text"log"_3(1)$ = 0.

B

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

C

$\text"log"_2(2)$ = 4.

D

$\text"log"(3 + 8 + 2)$ = $\text"log"(48)$.

Soln.
Ans: a

Speaking factually, $\text"log"_m(1)$ = 0 because m0 = 1 always, hence the answer. Expressions of the form $\text"log"_m(n) = p$ are same as mp = n. We can see that none of the options makes it correct. Also, log(m + n + p) = log(m × n × p) is possible only if m × n × p = m + n + p.

### Question 5

Suppose for the sake of this question that $\text"log"_2(5)$ = 10. Then what is $\text"log"_5(32)$?

A

1/2.

B

$\text"log"_2(5)$.

C

$\text"log"_5(2)$.

D

2.

Soln.
Ans: a

$\text"log"_5(32)$ is same as $\text"log"_5(2^5)$ = 5 × $\text"log"_5(2)$ = $5/{\text"log"_2(5)}$, which is same as $5/10$ = 1/2. This Blog Post/Article "Logarithms Quiz Set 010" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2020-02-07. Published on: 2016-05-08