# Logarithms Quiz Set 020

### Question 1

What is ${\text"log"(√7)}/{\text"log"(7)}$?

A

1/2.

B

$\text"log"_7(√7)$.

C

$\text"log"_√7(7)$.

D

2.

Soln.
Ans: a

${\text"log"(√7)}/{\text"log"(7)}$ is same as ${\text"log"(7^{1/2})}/{\text"log"(7)}$, which is same as (1/2) × ${\text"log"(7)}/{\text"log"(7)}$ = 1/2.

### Question 2

Which of these is correct?

A

$\text"log"_8(7)$ = $1/{\text"log"_7(8)}$.

B

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

C

$\text"log"_4(4)$ = 16.

D

$\text"log"(8 + 7 + 4)$ = $\text"log"(224)$.

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

What is x if logx$(5/3)$ = $1/2$?

A

$2{7/9}$.

B

$1{2/3}$.

C

$√{5/3}$.

D

$√{3/5}$.

Soln.
Ans: a

logx$(5/3)$ = $1/2$, by definition, gives $x^{1/2}$ = $5/3$. So x = $(5/3)^2$ = ${25/9}$, which is same as: $2{7/9}$.

### Question 4

What is log$7$ + log$1/7$?

A

0.

B

$\text"log"_3(7)$.

C

$\text"log"_7(3)$.

D

1/2.

Soln.
Ans: a

log(m) + log(1/m) = log (m × $1/m$) = log 1 = 0.

### Question 5

What is x if logx$(2/4)$ = $1/2$?

A

${1/4}$.

B

${1/2}$.

C

$√{1/2}$.

D

$√{2/1}$.

Soln.
Ans: a

logx$(2/4)$ = $1/2$, by definition, gives $x^{1/2}$ = $2/4$. So x = $(2/4)^2$ = ${1/4}$. 