# Logarithms Quiz Set 002

### Question 1

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 = ${3/5}$.

### Question 2

What is the value of $\text"log"_4(√4)$?

A

$1/2$.

B

$2$.

C

$\text"log"_√4(4)$.

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 3

If log(125) = 3, what is log(25)?

A

2.

B

$\text"log"_25(5)$.

C

$\text"log"_5(125)$.

D

1/2.

Soln.
Ans: a

We have 3 = log125 = log$5^3$ = 3 log 5, which gives log5 = 1. So, 2 = 2 × log5 = log$5^2$ = log25. Hence, the answer is 2.

### Question 4

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 5

If log(125) = 3, what is log(25)?

A

2.

B

$\text"log"_25(5)$.

C

$\text"log"_5(125)$.

D

1/2.

Soln.
Ans: a

We have 3 = log125 = log$5^3$ = 3 log 5, which gives log5 = 1. So, 2 = 2 × log5 = log$5^2$ = log25. Hence, the answer is 2.