# Logarithms Quiz Set 012

### Question 1

Which of these is correct?

A

$\text"log"_2(4)$ = $1/{\text"log"_4(2)}$.

B

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

C

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

D

$\text"log"(2 + 4 + 5)$ = $\text"log"(40)$.

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 2

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 3

What is x if logx$(2/7)$ = $1/2$?

A

${4/49}$.

B

${2/7}$.

C

$√{2/7}$.

D

$√{7/2}$.

Soln.
Ans: a

logx$(2/7)$ = $1/2$, by definition, gives $x^{1/2}$ = $2/7$. So x = $(2/7)^2$ = ${4/49}$.

### Question 4

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 5

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

A

$2{1/2}$.

B

$6{1/4}$.

C

$√{5/2}$.

D

$√{2/5}$.

Soln.
Ans: a

logx$(5/2)$ = 1, by definition, gives $x^1$ = $5/2$. So x = ${5/2}$, which is same as: $2{1/2}$.