Question

solve the exponential equation (√2)^x=2^8

Answer 1

(√2)^x=2^8
(√2)²^x=2²×^8. (multiplying 2 in power)
(2)^x=2^16. (base are same)
x=16

Answer 2

The value of x is 16.

Step-by-step explanation:

The given exponential equation,

$\sqrt{2} ^{x} =2^{8}$

To find, the vaue of x = ?

∴ $\sqrt{2} ^{x} =2^{8}$

⇒ $\sqrt{2} ^{x} =(\sqrt{2}\times \sqrt{2})^{8}$

⇒ $\sqrt{2} ^{x} =(\sqrt{2}^{2})^{8}$

⇒ $\sqrt{2} ^{x} =(\sqrt{2})^{2\times 8} =(\sqrt{2})^{16}$

[ ∵ $a^{m} \times a^{n} =a^{m+n}$]

Equating the power, we get

x = 16

Hence, the value of x is 16.