Logarithms

Q.

$5^4=625$ can also be expressed as

1. $lo{g}_{4}5=625$

2. $lo{g}_{5}625=4$

3. $lo{g}_{4}625=5$

4. $\sqrt[4]{4625}=5$

Q.

S1 : Logarithm of a number x is defined for all negative values of x.
S2 : Logarithm of 1 to the base x (where x>1) = 0

1. S1 is false, S2 is true
2. S1 is false, S2 is false
3. S1 is true, S2 is true

4. S1 is true, S2 is false

Q.

If $A=lo{g}_2\left(lo{g}_2\right(lo{g}_{4}256\left)\right)+2lo{g}_{\sqrt{2}}2$, then A is equal to

1. 7

2. 2

3. 3

4. 5

Q.

The number $lo{g}_{2}7$ is

1. a rational number.

2. a irrational number.

3. a prime number.

4. an integer.

Q.

Which is the correct order for a given number $\alpha$ in increasing order?

1. $lo{g}_2\alpha ,lo{g}_3\alpha ,lo{g}_e\alpha ,lo{g}_{10}\alpha$

2. $lo{g}_{10}\alpha ,lo{g}_3\alpha ,lo{g}_e\alpha ,lo{g}_2\alpha$

3. $lo{g}_{10}\alpha ,lo{g}_e\alpha ,lo{g}_2\alpha ,lo{g}_3\alpha$

4. $lo{g}_3\alpha ,lo{g}_e\alpha ,lo{g}_2\alpha ,lo{g}_{10}\alpha$

Q.

If $lo{g}_{x}y=100$ and $lo{g}_{2}x=10$, then the value of y is

1. ${1000}^2$

2. $2^{100}$

3. $2^{1000}$

4. $2^{10000}$

Q.

What is the value of $lo{g}_{\frac{1}{3}}9\sqrt{3}$

1. $\frac{2}{5}$

2. $\frac{5}{2}$

3. $\frac{-2}{5}$

4. $\frac{-5}{2}$

Q. $\log abc=loga+logb-logc$

1. True
2. False

Q. If a, b, c are three real numbers such that $a^b=c$ then b is called the base of c.

1. False
2. True

Q. If $y=27{\left(m\right)}^4$, then $\log y=4\log m+3\log 3$.

1. True
2. False