Question

Evaluate:- z = log(base √7 ) [ { √(8 + √28 )} - 1 ] .​

Answer 1

Answer:

z = {(sqrt(8 + 2 sqrt(7)) - 1) log(2.646 bp (base pairs))}

Explanation:

Answer 2

Answer:

→ z = 1.

Explanation:

$\sf \because z = log_{ \sqrt{7} }(( \sqrt{8 + \sqrt{28} } ) - 1) .$

Now, we have

$\sf \because \sqrt{8 + \sqrt{28} } . \\ \\ \sf = \sqrt{8 + 2 \sqrt{7} } . \\ \\ \sf = \sqrt{ {( \sqrt{7}) }^{2} + {1}^{2} + 2(1)( \sqrt{7} )} . \\ \\ \sf = \sqrt{ {( \sqrt{7} + 1)}^{2} } . \\ \\ \sf = | \sqrt{7 + 1} | . \\ \\ \sf = ( \sqrt{7} + 1).$

Now,

$\sf \because z = log_{ \sqrt{7} }(( \sqrt{8 + \sqrt{28} } ) - 1) . \\ \\ \implies \sf z = log_{ \sqrt{7} }( \sqrt{7} + 1 - 1) . \\ \\ \implies \sf z = log_{ \sqrt{7} }( \sqrt{7} ) . \\ \\ \implies \sf { \sqrt{7} }^{z} = \sqrt{7} . \\ \\ \boxed{ \therefore \it \pink{ z = 1.}}$

Hence, it is solved.