# Surds and Indices Quiz Set 004

### Question 1

What is x if \$3^x = 27\$?

A

3.

B

4.

C

2.

D

5.

Soln.
Ans: a

We can write the given expression as \$3^x = 3^3\$. The bases are same so powers should be same. Comparing we get x = 3.

### Question 2

What is \$26^0.24 × 26^x = 26^0.15\$?

A

-0.09.

B

0.41.

C

1.41.

D

1.91.

Soln.
Ans: a

We can simplify the given expression to \$26^{0.24 + x} = 26^0.15\$. The bases are equal, so the powers should also be equal. Hence \$0.24 + x = 0.15\$ which gives x = -0.09.

### Question 3

What is \$16^0.15 × 16^0.1\$?

A

2.

B

3.

C

5.

D

4.

Soln.
Ans: a

By inspection, we get \$(2^4)^0.15 × (2^4)^0.1\$, which equals \$(2^4)^(0.15 + 0.1)\$, which equals \$(2^4)^0.25\$, which equals \$2^1\$, or 2. Note: The trick in such type of questions is to keep an eye on the "bases".

### Question 4

What is x if \$6^x = 36\$?

A

2.

B

3.

C

5.

D

4.

Soln.
Ans: a

We can write the given expression as \$6^x = 6^2\$. The bases are same so powers should be same. Comparing we get x = 2.

### Question 5

What is \$({19/28})^0.12 × ({19/28})^x = ({19/28})^0.11\$?

A

-0.00999999999999998.

B

0.49.

C

1.49.

D

1.99.

Soln.
Ans: a

We can simplify the given expression to \$({19/28})^{0.12 + x} = ({19/28})^0.11\$. The bases are equal, so the powers should also be equal. Hence \$0.12 + x = 0.11\$ which gives x = -0.00999999999999998.