Logarithms Quiz Set 019

Question 1

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.

Question 2

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

A

0.

B

$\text"log"_2(7)$.

C

$\text"log"_7(2)$.

D

1/2.

Soln.
Ans: a

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

Question 3

If log(125) = 3, what is log(25)?

A

2.

B

$\text"log"_25(5)$.

C

$\text"log"_5(125)$.

D

1/2.

Soln.
Ans: a

We have 3 = log125 = log$5^3$ = 3 log 5, which gives log5 = 1. So, 2 = 2 × log5 = log$5^2$ = log25. Hence, the answer is 2.

Question 4

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 5

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 = ${4/7}$.