Logarithms Quiz Set 018

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Question 1

Suppose for the sake of this question that $\text"log"_3(2)$ = 4. Then what is $\text"log"_2(9)$?

 A

1/2.

 B

$\text"log"_3(2)$.

 C

$\text"log"_2(3)$.

 D

2.

Soln.
Ans: a

$\text"log"_2(9)$ is same as $\text"log"_2(3^2)$ = 2 × $\text"log"_2(3)$ = $2/{\text"log"_3(2)}$, which is same as $2/4$ = 1/2.


Question 2

Let us suppose that $\text"log"_3(4)$ = 4, then what is $\text"log"_4(3)$?

 A

$1/4$.

 B

$4$.

 C

$\text"log"_4(√4)$.

 D

5.

Soln.
Ans: a

From the theory of logarithms, we know that $\text"log"_4(3)$ = $1/{\text"log"_3(4)}$ = $1/4$.


Question 3

What is $1/{\text"log"_3(60)}$ + $1/{\text"log"_4(60)}$ + $1/{\text"log"_5(60)}$?

 A

$1$.

 B

5.

 C

12.

 D

0.

Soln.
Ans: a

The given expression simplifies to $\text"log"_60(3)$ + $\text"log"_60(4)$ + $\text"log"_60(5)$ = $\text"log"_60(3 × 4 × 5)$ = $\text"log"_60(60)$ = 1.


Question 4

Which of these is correct?

 A

$\text"log"_6(2)$ = $1/{\text"log"_2(6)}$.

 B

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

 C

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

 D

$\text"log"(6 + 2 + 4)$ = $\text"log"(48)$.

Soln.
Ans: a

Speaking factually, $\text"log"_m(n)$ = $1/{\text"log"_n(m)}$, 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 $\text"log"_2(7)$ = 14. Then what is $\text"log"_7(128)$?

 A

1/2.

 B

$\text"log"_2(7)$.

 C

$\text"log"_7(2)$.

 D

2.

Soln.
Ans: a

$\text"log"_7(128)$ is same as $\text"log"_7(2^7)$ = 7 × $\text"log"_7(2)$ = $7/{\text"log"_2(7)}$, which is same as $7/14$ = 1/2.


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This Blog Post/Article "Logarithms Quiz Set 018" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2019-08-18.

Posted by Parveen(Hoven),
Aptitude Trainer


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