Question

solve this.............​

Answer 1

Answer:

x = 16

Explanation:

Given: (√2)ˣ = 2⁸

or $(2)^{x/2} = 2^{8}$

⇒ x/2 = 8

or x = 16

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Answer 2

Question :

Find the value of x

$\rm\:(\sqrt{2})^x=2^8$

Formula's :

• Properties of Exponents:

$\sf1)a^m\times\:a^n=a^{m+n}$

$\sf2)\frac{a^m}{a^n}=a^{m-n}$

$\sf3)a^m\:\times\:b^m=(ab)^m$

$\sf4)a^{0}=1$

$\sf5)(a^m)^n=a^{mn}$

Solution :

We have ,

$\rm\:(\sqrt{2})^x=2^8$

$\sf\implies\:(2^{\frac{1}{2}})^x=2^8$

We know that

$\sf\:(a^m)^n=a^{mn}$

$\sf\implies\:(2)^{\frac{x}{2}}=2^8$

On Comparing

$\sf\:\dfrac{x}{2}=8$

$\sf\implies\:x=8\times2$

$\sf\implies\:x=16$

Therefore, the value of x is 16