# Logarithms Quiz Set 006

### Question 1

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 2

Which of these is correct?

A

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

B

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

C

$\text"log"_2(2)$ = 4.

D

$\text"log"(4 + 6 + 2)$ = $\text"log"(48)$.

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.

### Question 3

What is the value of $\text"log"_2(√2)$?

A

$1/2$.

B

$2$.

C

$\text"log"_√2(2)$.

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 4

Suppose for the sake of this question that $\text"log"_2(7)$ = 14. Then what is $\text"log"_7(128)$?

A

1/2.

B

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

C

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

D

2.

Soln.
Ans: a

$\text"log"_7(128)$ is same as $\text"log"_7(2^7)$ = 7 × $\text"log"_7(2)$ = $7/{\text"log"_2(7)}$, which is same as $7/14$ = 1/2.

### Question 5

What is x if logx(y) = 7 and log2(x) = 2?

A

74.

B

$√4$.

C

$√{7/2}$.

D

$√{2/7}$.

Soln.
Ans: a

By definition, log2(x) = 2 gives x = 22 = 4. We are also given logx(y) = 7, which gives y = 7x = 74.