Question

find the value of x if under root 6 raise to power x is equal to 6 raise to power 4​

Answer 1

Answer:

8

Step-by-step explanation:

√6^x=6^4

6^x=6^4*2

6^x=6^8

x=8

Answer 2

The value of x = 8

Step-by-step explanation:

We have,

$\sqrt{6}^{x} =6^{4}$

To find, the value of x =?

∴ $\sqrt{6}^{x} =6^{4}$

Since, 6 = $\sqrt{6}$ × $\sqrt{6}$

$\sqrt{6}^{x} =(\sqrt{6}\times \sqrt{6})^{4}$

Using the identity,

$a^{m} +a^{m} =a^{2m}$

⇒ $\sqrt{6}^{x} =(\sqrt{6}^{1+1})^{4}$

⇒ $\sqrt{6}^{x} =(\sqrt{6}^{2})^{4}$

Using the exponential identity,

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

⇒ $\sqrt{6}^{x} =\sqrt{6}^{2\times 4}$

⇒ $\sqrt{6}^{x} =\sqrt{6}^{8}$

The base are same, then comparing the powers of $\sqrt{6}$, we get

⇒ x = 8

Thus, the value of x = 8