# Logarithms Quiz Set 005

### 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 = $1{5/11}$.