Logarithms Quiz Set 016 | Maths Aptitude Quiz Questions and Mock Test on Logarithms Set 16 | mock tests for Bank PO, SSC Exams, SO Clerical Exam, GATE Exam, LIC AO, GIC AO, etc.

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Question 1

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

log($2/3$).

log($3/2$).

log₂(3).

log₃(2).

Soln.
Ans: a

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

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Question 2

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

1/2.

$\text"log"_6(√6)$.

$\text"log"_√6(6)$.

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.

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Question 3

Which of these is correct?

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

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

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

$\text"log"_7(1)$ = 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 m^p = n. We can see that none of the other options makes it correct.

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Question 4

Which of these is correct?

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

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

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

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

Soln.
Ans: a

Expressions of the form $\text"log"_m(n) = p$ are same as m^p = 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.

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