# Logarithms Quiz Set 004

### Question 1

What is x if logx(y) = 5 and log2(x) = 3?

A

58.

B

$√8$.

C

$√{5/3}$.

D

$√{3/5}$.

Soln.
Ans: a

By definition, log2(x) = 3 gives x = 23 = 8. We are also given logx(y) = 5, which gives y = 5x = 58.

### Question 2

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

$\text"log"_8(1)$ = 8.

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 3

Let us suppose that $\text"log"_3(4)$ = 4, then what is $\text"log"_4(3)$?

A

$1/4$.

B

$4$.

C

$\text"log"_4(√4)$.

D

5.

Soln.
Ans: a

From the theory of logarithms, we know that $\text"log"_4(3)$ = $1/{\text"log"_3(4)}$ = $1/4$.

### Question 4

If log(343) = 3, what is log(49)?

A

2.

B

$\text"log"_49(7)$.

C

$\text"log"_7(343)$.

D

1/2.

Soln.
Ans: a

We have 3 = log343 = log$7^3$ = 3 log 7, which gives log7 = 1. So, 2 = 2 × log7 = log$7^2$ = log49. Hence, the answer is 2.

### Question 5

What is x if logx(y) = 5 and log2(x) = 3?

A

58.

B

$√8$.

C

$√{5/3}$.

D

$√{3/5}$.

Soln.
Ans: a

By definition, log2(x) = 3 gives x = 23 = 8. We are also given logx(y) = 5, which gives y = 5x = 58.