Question

If √2^n = 4, then n = _____​

Answer 1

$(√2)^n = 4 \\ = > {(2)}^{ \frac{1}{2} \times n} = {2}^{2} \\ = > \frac{n}{2 } = 2 \\ = > n = 2 \times 2 \\ \\ = > n = 4$

Answer 2

Question:-

If ${( \sqrt{2} )}^{n} = 4$ .Then, n =

Solution:-

Given,

$( { \sqrt{2}) }^{n} = 4$

$4 = {2}^{2}$

$\sqrt{2} = {2}^{ \frac{1}{2} }$

Substitute it in given

${2}^{ \frac{n}{2} } = {2}^{2}$

Bases are equal. So, powers also equal

$\frac{n}{2} = 2$

$n = 2 \times 2$

$n = 4$

Final Answer:-

The value of n is 4