Question

pls check the attachment​

Answer 1

Answer:

Answer is 80 as

$10 {}^{ \frac{x}{2} + 1} = 10 {}^{ \frac{x}{2} } \times 10 \\ = 8 \times 10 = 80$

Hence in this way your answer is 80

Answer 2

${ \bold{ \boxed{ \boxed{ \red{ANSWER}}}}}$

${ \bold{ \underline{Given } : - }} \\ \\ { \bold{ \boxed{\orange{ {10}^{x} = 64 }}}} \\ \\ { \bold { \underline{To \: \: find } : - }} \\ \\ { \bold{ \boxed{\orange{ {10}^{ \frac{x}{2} + 1}}}}} \\ \\ { \bold{ \boxed{\green{ \star \: Solution }}}} \\ \\ { \bold{ \pink{ \mathtt{ : \implies {10}^{x} = 64}}}} \\ \\{ \bold{ \red{take \: \: square \: \: root \: \: both \: \: side - }}} \\ \\ { \bold{ \pink{ \mathtt{ : \implies \sqrt{ {10}^{x} } = \sqrt{64} }}}} \\ \\ { \bold{ \pink{ \mathtt{ : \implies {10}^{ \frac{x}{2} } = 8 }}}} \\ \\ { \bold{ \red{now \: \: multiply \: \: of \: \: 10 \: \: in \: \: both \: \: side - }}} \\ \\ { \bold{ \pink{ \mathtt{ : \implies {10}^{ \frac{x}{2} } \times 10 = 8 \times 10 }}}} \\ \\ { \bold{ \pink{ \mathtt{ : \implies { \boxed{{10}^{ \frac{x}{2} + 1} = 80}}}}}} \\ \\ { \bold{ \pink{ \mathtt{ so \: \: that \: \: option(c) \: \: is \: \: correct}}}}$