Logarithms Quiz Set 005

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Question 1

Let us suppose that $\text"log"_2(3)$ = 3, then what is $\text"log"_3(2)$?

 A

$1/3$.

 B

$3$.

 C

$\text"log"_3(√3)$.

 D

4.

Soln.
Ans: a

From the theory of logarithms, we know that $\text"log"_3(2)$ = $1/{\text"log"_2(3)}$ = $1/3$.


Question 2

What is the value of log(2) - log(7)?

 A

log($2/7$).

 B

log($7/2$).

 C

log2(7).

 D

log7(2).

Soln.
Ans: a

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


Question 3

What is x if logx$(6/7)$ = 1?

 A

${6/7}$.

 B

${36/49}$.

 C

$√{6/7}$.

 D

$√{7/6}$.

Soln.
Ans: a

logx$(6/7)$ = 1, by definition, gives $x^1$ = $6/7$. So x = ${6/7}$.


Question 4

What is P if $\text"log"_3(4)$ + $\text"log"_3(4P + 1)$ = 1 + $\text"log"_3(P + 4)$?

 A

${8/13}$.

 B

$1{3/4}$.

 C

$2{4/15}$.

 D

$3{2/15}$.

Soln.
Ans: a

We have $\text"log"_3(4)$ + $\text"log"_3(4P + 1)$ = $\text"log"_3(3)$ + $\text"log"_3(P + 4)$. It is same as $\text"log"_3(4 × (4P + 1))$ = $\text"log"_3(3 × (P + 4))$. Equating the logs, $4 × (4P + 1) = 3 × (P + 4)$, solving for P we get P = ${8/13}$.


Question 5

What is P if $\text"log"_5(4)$ + $\text"log"_5(4P + 1)$ = 1 + $\text"log"_5(P + 4)$?

 A

$1{5/11}$.

 B

$2{7/10}$.

 C

${5/13}$.

 D

$3{10/13}$.

Soln.
Ans: a

We have $\text"log"_5(4)$ + $\text"log"_5(4P + 1)$ = $\text"log"_5(5)$ + $\text"log"_5(P + 4)$. It is same as $\text"log"_5(4 × (4P + 1))$ = $\text"log"_5(5 × (P + 4))$. Equating the logs, $4 × (4P + 1) = 5 × (P + 4)$, solving for P we get P = $1{5/11}$.


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This Blog Post/Article "Logarithms Quiz Set 005" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-05-17.

Posted by Parveen(Hoven),
Aptitude Trainer


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