# Logarithms Quiz Set 020

### Question 1

What is x if logx$(3/5)$ = $1/2$?

A

${9/25}$.

B

${3/5}$.

C

$√{3/5}$.

D

$√{5/3}$.

Soln.
Ans: a

logx$(3/5)$ = $1/2$, by definition, gives $x^{1/2}$ = $3/5$. So x = $(3/5)^2$ = ${9/25}$.

### Question 2

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 3

Which of these is correct?

A

$\text"log"(1 + 2 + 3)$ = $\text"log"(1 × 2 × 3)$.

B

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

C

$\text"log"_6(6)$ = 36.

D

$\text"log"_7(1)$ = 7.

Soln.
Ans: a

Speaking factually, log(m + n + p) = log(m × n × p) is possible only if m × n × p = m + n + p, hence the answer, because 1 × 2 × 3 = 1 + 2 + 3. Expressions of the form $\text"log"_m(n) = p$ are same as mp = n. We can see that none of the other options makes it correct.

### Question 4

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 5

What is the value of $\text"log"_3(√3)$?

A

$1/2$.

B

$2$.

C

$\text"log"_√3(3)$.

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.