# 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 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

Which of these is correct?

A

$\text"log"_6(8)$ = $1/{\text"log"_8(6)}$.

B

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

C

$\text"log"_4(4)$ = 16.

D

$\text"log"(6 + 8 + 4)$ = $\text"log"(192)$.

Soln.
Ans: a

Speaking factually, $\text"log"_m(n)$ = $1/{\text"log"_n(m)}$, 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 log$4/3$ + log$3/4$?

A

0.

B

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

C

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

D

1/2.

Soln.
Ans: a

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

### Question 5

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 $\text"log"_3(2)$ = $1/{\text"log"_2(3)}$ = $1/3$. 