# Logarithms Quiz Set 013

### Question 1

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

$\text"log"_2(1)$ = 2.

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 2

What is log$5/4$ + log$4/5$?

A

0.

B

$\text"log"_4(5)$.

C

$\text"log"_5(4)$.

D

1/2.

Soln.
Ans: a

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

### Question 3

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 4

What is the value of log(2) - log(7)?

A

log($2/7$).

B

log($7/2$).

C

log2(7).

D

log7(2).

Soln.
Ans: a

log($m/n$) = log(m) - log(n) always.

### Question 5

What is x if logx(y) = 6 and log2(x) = 5?

A

632.

B

$√32$.

C

$√{6/5}$.

D

$√{5/6}$.

Soln.
Ans: a

By definition, log2(x) = 5 gives x = 25 = 32. We are also given logx(y) = 6, which gives y = 6x = 632.