Question

(under root 2) power x =2 power 8​

Answer 1

Answer:

$( { \sqrt{2} })^{x} = {2}^{8} \\ squiring \: both \: sides \\ { (\sqrt{2}) }^{2x} = {2}^{2 \times 8} \\ \therefore \: {2}^{x} = {2}^{16} \\ \huge \fbox{ \therefore \:x = 16} \\ \\ alternate \: method \\ ( { \sqrt{2} })^{x} = {2}^{8} \\ \therefore \: ({2}^{ \frac{1}{2} } ) ^{x} = {2}^{8} \\ \therefore \: {2}^{ \frac{x}{2} } = {2}^{8} \\ \therefore \: \frac{x}{2} = 8 \\ \therefore \: x = 2 \times 8 \\ \huge \fbox{ \therefore \:x = 16}$