Question

4^4a-12 =1/16^a what is the value of a ?​

Answer 1

Answer:

4∧4a - 12 = 1 ÷ 16 ∧ a

4∧4a - 12 = 1 ÷ 4 ∧ 2a

4∧4a - 12 = 4 ∧ -2a

∴ 4a - 12 = -2a

  6a = 12

∴ a = 2

Answer 2

The value of 'a' is equal to '2'.

Step-by-step explanation:

We have,

$4^{4a-12} =\dfrac{1}{16^a}$

To find, the value of a = ?

∴ $4^{4a-12} =\dfrac{1}{16^a}$

⇒ $4^{4a-12} =16^{-a}$

Using the identity,

$a^{-m} =\dfrac{1}{a^{m}}$

⇒ $4^{4a-12} =(4^2)^{-a}$

Using the identity,

$(a^m)^{n}=a^{mn}$

⇒ $4^{4a-12} =4^{-2a}$

Equating the powers of 4, we get

4a - 12 = - 2a

⇒ 4a + 2a = 12

⇒ 6a = 12

⇒ a = $\dfrac{12}{6}$

⇒ a = 2

Thus, the value of 'a' is equal to '2'.