Base

Q.

If $a^x=b^y=c^z$ and $b^2=ac$ then $\frac{1}{x}+\frac{1}{z}=\frac{1}{y}$

1. True

2. False

Q. Based on the definition of logarithms, what is ${\log }_{10}1000$?

1. 100
2. 3
3. 4
4. 10

Q. The multiplicative inverse of ${10}^{-5}$ is

1. - 50
2. 0.00001
3. - 1, 00, 000
4. 1, 00, 000

Q. Choose the pair which has the same base.

1. 5^6, 5^4
2. 4^5, 6^5
3. 3^6, 6^3
4. 4^2, 2^6

Q. Identify the region which represents the power $2^2.$

1. 
2. 
3. 

Q. Determine the signs of the following numbers.
$lo{g}_{3}4-lo{g}_{4}3$

Q. The multiplicative inverse of $2^2$ is

1. $\frac{1}{4}$
2. $\frac{2}{10}$
3. $\frac{1}{16}$
4. $\frac{1}{2}$

Q. State true or false:

1. True
2. False

Q. If ${\log }_{4}5=a$ and ${\log }_{5}6=b$ then ${\log }_{3}2$ is equal to

1. $\frac{1}{2b+1}$
2. $\frac{1}{2a+1}$
3. $2ab+1$
4. $\frac{1}{2ab-1}$

Q. If we represent 343 in exponential form , then the base is and the exponent is .

1. 7
2. 3
3. 9
4. 19

Q. In 2n, n is known as a/an .

1. base
2. exponent
3. constant
4. alphabet

Q. 2 multiplied by itself ten times, when written in the exponential form is .

1. $2\times 10$
2. $2\times 2^8$
3. $2^{10}$
4. $2^{-10}$

Q. The value of $2^8$ is .

1. 128
2. 256
3. 512
4. 64