# Logarithms Quiz Set 001

### Question 1

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

$\text"log"_2(1)$ = 2.

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 2

Let us suppose that log(5) = 3, then what is log($1/50$) if the base is 10?

A

-4.

B

$\text"log"_3(50)$.

C

$\text"log"_5(30)$.

D

4.

Soln.
Ans: a

We know log($1/{10m}$) = log(1) - (log(10) + log(m)) = 0 - (1 + 3) = -4.

### Question 3

What is P if $\text"log"_5(4)$ + $\text"log"_5(4P + 1)$ = 1 + $\text"log"_5(P + 4)$?

A

$1{5/11}$.

B

$2{7/10}$.

C

${5/13}$.

D

$3{10/13}$.

Soln.
Ans: a

We have $\text"log"_5(4)$ + $\text"log"_5(4P + 1)$ = $\text"log"_5(5)$ + $\text"log"_5(P + 4)$. It is same as $\text"log"_5(4 × (4P + 1))$ = $\text"log"_5(5 × (P + 4))$. Equating the logs, $4 × (4P + 1) = 5 × (P + 4)$, solving for P we get P = $1{5/11}$.

### Question 4

What is x if logx(y) = 6 and log2(x) = 5?

A

632.

B

$√32$.

C

$√{6/5}$.

D

$√{5/6}$.

Soln.
Ans: a

By definition, log2(x) = 5 gives x = 25 = 32. We are also given logx(y) = 6, which gives y = 6x = 632.

### Question 5

Suppose for the sake of this question that $\text"log"_2(5)$ = 10. Then what is $\text"log"_5(32)$?

A

1/2.

B

$\text"log"_2(5)$.

C

$\text"log"_5(2)$.

D

2.

Soln.
Ans: a

$\text"log"_5(32)$ is same as $\text"log"_5(2^5)$ = 5 × $\text"log"_5(2)$ = $5/{\text"log"_2(5)}$, which is same as $5/10$ = 1/2.