Q5 of 239 Page 25

If 2^x = 16, find
i. x

ii.

iii. 2^2x

iv. 2^{x + 2}

v.

i. 2^x = 16

⇒ 2^x = 2⁴

⇒ x = 4 (∵ base is same)

ii.

iii. 2^2x = 2^{2× 4}

⇒ 2^2x = 2⁸

⇒ 2^2x = (2× 2× ……8 times)

⇒ 2^2x = 256

iv. 2^{x + 2} = 2^{4 + 2}

⇒ 2^{x + 2} = 2⁶

⇒ 2^{x + 2} = 2× 2× 2× 2× 2× 2

⇒ 2^{x + 2} = 64

v. √2^-x = √2^-4

Find the value of m for which

(5^m)² × (25)³ × 125² = 1

Find the value of m for which

If 3^x = 81, find

i. x

ii. 3^{x + 3}

iii. 3^x/2

iv. 3^2x

v. 3^{x – 6}

Prove that

Questions · 239

1. Real Number System

1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 5 5 6 6 1 1 1 1 2 2 2 2 3 3 3 3 1 1 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 6 6 1 2 2 2 2 2 3 3 3 4 4 4 4 5 5 5 5 5 6 6 6 6 6 6 7 7 1 1 1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 6 6 6 6 6 7 7 7 7 7 8 8 8 8 8 9 10 10 10 10 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 6 6 6 7 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 1 1 1 1 1 1 1 2 3

If 2x = 16, findi. xii. iii. 22xiv. 2x + 2v.