Logarithms Quiz Set 016

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Question 1

What is the value of log(2) - log(3)?

 A

log($2/3$).

 B

log($3/2$).

 C

log2(3).

 D

log3(2).

Soln.
Ans: a

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


Question 2

What is ${\text"log"(√6)}/{\text"log"(6)}$?

 A

1/2.

 B

$\text"log"_6(√6)$.

 C

$\text"log"_√6(6)$.

 D

2.

Soln.
Ans: a

${\text"log"(√6)}/{\text"log"(6)}$ is same as ${\text"log"(6^{1/2})}/{\text"log"(6)}$, which is same as (1/2) × ${\text"log"(6)}/{\text"log"(6)}$ = 1/2.


Question 3

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

$\text"log"_7(1)$ = 7.

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 4

Which of these is correct?

 A

$\text"log"_2(2)$ = 1.

 B

$\text"log"_5(5)$ = 5.

 C

$\text"log"_3(3)$ = 9.

 D

$\text"log"(2 + 5 + 3)$ = $\text"log"(30)$.

Soln.
Ans: a

Expressions of the form $\text"log"_m(n) = p$ are same as mp = n. We can see that if m = n, then p = 1 will make it correct. Also, log(m + n + p) = log(m × n × p) is possible only if m × n × p = m + n + p.


Question 5

If log(343) = 3, what is log(49)?

 A

2.

 B

$\text"log"_49(7)$.

 C

$\text"log"_7(343)$.

 D

1/2.

Soln.
Ans: a

We have 3 = log343 = log$7^3$ = 3 log 7, which gives log7 = 1. So, 2 = 2 × log7 = log$7^2$ = log49. Hence, the answer is 2.


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This Blog Post/Article "Logarithms Quiz Set 016" 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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