# Logarithms Quiz Set 014

### 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

$\text"log"_6(2)$ = $1/{\text"log"_2(6)}$.

B

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

C

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

D

$\text"log"(6 + 2 + 5)$ = $\text"log"(60)$.

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 3

Which of these is correct?

A

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

B

$\text"log"_7(7)$ = 7.

C

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

D

$\text"log"(4 + 7 + 2)$ = $\text"log"(56)$.

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 4

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 5

What is x if logx$(3/5)$ = 1?

A

${3/5}$.

B

${9/25}$.

C

$√{3/5}$.

D

$√{5/3}$.

Soln.
Ans: a

logx$(3/5)$ = 1, by definition, gives $x^1$ = $3/5$. So x = ${3/5}$.