Logarithms Quiz Set 006

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Question 1

What is x if logx$(4/7)$ = 1?

 A

${4/7}$.

 B

${16/49}$.

 C

$√{4/7}$.

 D

$√{7/4}$.

Soln.
Ans: a

logx$(4/7)$ = 1, by definition, gives $x^1$ = $4/7$. So x = ${4/7}$.


Question 2

Which of these is correct?

 A

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

 B

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

 C

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

 D

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

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 3

What is the value of $\text"log"_2(√2)$?

 A

$1/2$.

 B

$2$.

 C

$\text"log"_√2(2)$.

 D

0.

Soln.
Ans: a

From the theory of logarithms, we know that $\text"log"_m(√m)$ = $1/2$ × $\text"log"_m(m)$ = $1/2$ × 1 = 1/2.


Question 4

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.


Question 5

What is x if logx(y) = 7 and log2(x) = 2?

 A

74.

 B

$√4$.

 C

$√{7/2}$.

 D

$√{2/7}$.

Soln.
Ans: a

By definition, log2(x) = 2 gives x = 22 = 4. We are also given logx(y) = 7, which gives y = 7x = 74.


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This Blog Post/Article "Logarithms Quiz Set 006" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-04-07.

Posted by Parveen(Hoven),
Aptitude Trainer


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