Assertion (A):

4^x= 8^y x 16⁰
⇒ 2x = 3y

Reason (R):

4^x= 8^y x 16⁰
⇒ 2^2x = 2^3y
⇒ 2x = 3y
and 2x - 3y = 0

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.

Both A and R are true.

Explanation

Given,

4^x= 8^y x 16⁰

⇒ 2^(2x)= 2^(3y) x 2^{(4 x 0)}

⇒ 2^2x= 2^3y x 2⁰

⇒ 2^2x= 2^3y

⇒ 2x = 3y

∴ Assertion (A) is true.

Given,

4^x= 8^y x 16⁰

⇒ 2^(2x)= 2^(3y) x 2^{(4 x 0)}

⇒ 2^2x= 2^3y x 2⁰

⇒ 2^2x= 2^3y

⇒ 2x = 3y

⇒ 2x - 3y = 0

∴ Reason (R) is true.

Hence, both Assertion (A) and Reason (R) are true.