Question

pls answer I need it fast step by step
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Answer 1

Answer :-

Value of b is 32.

Explanation :-

$\sf log_{ \sqrt{8}}b = \dfrac{10}{3}$

$\sf \implies (\sqrt{8})^{ \dfrac{10}{3} } = b$

$\boxed{ \bf \because log_ an = x \implies {a}^{x} = n}$

$\sf \implies (8^{ \dfrac{1}{2} })^{ \dfrac{10}{3} } = b$

$\sf \implies 8^{ \dfrac{1}{2} \times \dfrac{10}{3} } = b$

$\boxed{ \bf \because ( {a}^{m}) ^n = a^{mn} }$

$\sf \implies 8^{ \dfrac{5}{3}} = b$

Cubing on both sides

$\sf \implies (8^{\dfrac{5}{3} })^3= b^3$

$\sf \implies 8^5 = b^3$

$\sf \implies 32768 = b^3$

$\sf \implies {32}^{3} = b^3$

Taking cube root on both sides

$\sf \implies 32 = b$

$\sf \implies b = 32$

∴ the value of b is 32.