# Logarithms Quiz Set 003

### Question 1

What is the value of log2(128)?

A

7.

B

$√7$.

C

0.

D

$√128$.

Soln.
Ans: a

Let log2(128) = P. By definition, we have 2P = 128 = 27, which gives 7 as the answer.

### Question 2

What is $1/{\text"log"_4(60)}$ + $1/{\text"log"_3(60)}$ + $1/{\text"log"_5(60)}$?

A

$1$.

B

5.

C

12.

D

0.

Soln.
Ans: a

The given expression simplifies to $\text"log"_60(4)$ + $\text"log"_60(3)$ + $\text"log"_60(5)$ = $\text"log"_60(4 × 3 × 5)$ = $\text"log"_60(60)$ = 1.

### Question 3

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 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 log$3/4$ + log$4/3$?

A

0.

B

$\text"log"_4(3)$.

C

$\text"log"_3(4)$.

D

1/2.

Soln.
Ans: a

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