# Logarithms Quiz Set 017

### Question 1

What is log$2/4$ + log$4/2$?

A

0.

B

$\text"log"_4(2)$.

C

$\text"log"_2(4)$.

D

1/2.

Soln.
Ans: a

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

### Question 2

What is x if logx$(4/7)$ = 1?

A

${4/7}$.

B

${16/49}$.

C

$√{4/7}$.

D

$√{7/4}$.

Soln.
Ans: a

logx$(4/7)$ = 1, by definition, gives $x^1$ = $4/7$. So x = ${4/7}$.

### Question 3

What is P if $\text"log"_5(3)$ + $\text"log"_5(3P + 1)$ = 1 + $\text"log"_5(P + 3)$?

A

3.

B

4.

C

2.

D

2.

Soln.
Ans: a

We have $\text"log"_5(3)$ + $\text"log"_5(3P + 1)$ = $\text"log"_5(5)$ + $\text"log"_5(P + 3)$. It is same as $\text"log"_5(3 × (3P + 1))$ = $\text"log"_5(5 × (P + 3))$. Equating the logs, $3 × (3P + 1) = 5 × (P + 3)$, solving for P we get P = 3.

### Question 4

Which of these is correct?

A

$\text"log"_6(2)$ = $1/{\text"log"_2(6)}$.

B

$\text"log"_2(2)$ = 2.

C

$\text"log"_5(5)$ = 25.

D

$\text"log"(6 + 2 + 5)$ = $\text"log"(60)$.

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

Which of these is correct?

A

$\text"log"_4(1)$ = 0.

B

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

C

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

D

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

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.