# Logarithms Quiz Set 015

### Question 1

Which of these is correct?

A

$\text"log"_2(1)$ = 0.

B

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

C

$\text"log"_8(8)$ = 64.

D

$\text"log"(2 + 7 + 8)$ = $\text"log"(112)$.

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 2

What is $1/{\text"log"_6(210)}$ + $1/{\text"log"_5(210)}$ + $1/{\text"log"_7(210)}$?

A

$1$.

B

7.

C

18.

D

0.

Soln.
Ans: a

The given expression simplifies to $\text"log"_210(6)$ + $\text"log"_210(5)$ + $\text"log"_210(7)$ = $\text"log"_210(6 × 5 × 7)$ = $\text"log"_210(210)$ = 1.

### Question 3

What is ${\text"log"(√6)}/{\text"log"(6)}$?

A

1/2.

B

$\text"log"_6(√6)$.

C

$\text"log"_√6(6)$.

D

2.

Soln.
Ans: a

${\text"log"(√6)}/{\text"log"(6)}$ is same as ${\text"log"(6^{1/2})}/{\text"log"(6)}$, which is same as (1/2) × ${\text"log"(6)}/{\text"log"(6)}$ = 1/2.

### Question 4

What is log$6/4$ + log$4/6$?

A

0.

B

$\text"log"_4(6)$.

C

$\text"log"_6(4)$.

D

1/2.

Soln.
Ans: a

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

### Question 5

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

A

0.

B

$\text"log"_2(7)$.

C

$\text"log"_7(2)$.

D

1/2.

Soln.
Ans: a

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