# Logarithms Quiz Set 009

### Question 1

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 = $1{5/11}$.

### Question 2

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 = $1{5/11}$.

### Question 3

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 4

What is ${\text"log"(√3)}/{\text"log"(3)}$?

A

1/2.

B

$\text"log"_3(√3)$.

C

$\text"log"_√3(3)$.

D

2.

Soln.
Ans: a

${\text"log"(√3)}/{\text"log"(3)}$ is same as ${\text"log"(3^{1/2})}/{\text"log"(3)}$, which is same as (1/2) × ${\text"log"(3)}/{\text"log"(3)}$ = 1/2.

### Question 5

What is the value of log(5) - log(3)?

A

log($5/3$).

B

log($3/5$).

C

log5(3).

D

log3(5).

Soln.
Ans: a

log($m/n$) = log(m) - log(n) always.