# Logarithms Quiz Set 005

### Question 1

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

A

0.

B

$\text"log"_3(7)$.

C

$\text"log"_7(3)$.

D

1/2.

Soln.
Ans: a

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

### Question 2

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 3

What is log$3/4$ + log$4/3$?

A

0.

B

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

C

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

D

1/2.

Soln.
Ans: a

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

### Question 4

What is the value of log(4) + log(5)?

A

log($4 × 5$).

B

log($5 + 4$).

C

log4(5).

D

log5(4).

Soln.
Ans: a

log(mn) = log(m) + log(n) always.

### 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.