Logarithms Quiz Set 014

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Question 1

What is x if logx(y) = 5 and log2(x) = 3?

 A

58.

 B

$√8$.

 C

$√{5/3}$.

 D

$√{3/5}$.

Soln.
Ans: a

By definition, log2(x) = 3 gives x = 23 = 8. We are also given logx(y) = 5, which gives y = 5x = 58.


Question 2

Which of these is correct?

 A

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

 B

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

 C

$\text"log"_5(5)$ = 25.

 D

$\text"log"(6 + 2 + 5)$ = $\text"log"(60)$.

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 3

Which of these is correct?

 A

$\text"log"_4(1)$ = 0.

 B

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

 C

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

 D

$\text"log"(4 + 7 + 2)$ = $\text"log"(56)$.

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 4

What is x if logx(y) = 5 and log2(x) = 3?

 A

58.

 B

$√8$.

 C

$√{5/3}$.

 D

$√{3/5}$.

Soln.
Ans: a

By definition, log2(x) = 3 gives x = 23 = 8. We are also given logx(y) = 5, which gives y = 5x = 58.


Question 5

What is x if logx$(3/5)$ = 1?

 A

${3/5}$.

 B

${9/25}$.

 C

$√{3/5}$.

 D

$√{5/3}$.

Soln.
Ans: a

logx$(3/5)$ = 1, by definition, gives $x^1$ = $3/5$. So x = ${3/5}$.


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This Blog Post/Article "Logarithms Quiz Set 014" 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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