Question

$log3 \sqrt{243 = }$
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Answer 1

${\huge{\fcolorbox{aqua}{gold}{\fcolorbox{black}{blue}{Answer\checkmark}}}}$

$\implies \: \rm \: log_{3} \: ( \sqrt{243} ) = x \\ \\ \implies \: \rm{3}^{x} = \sqrt{243} \\ \\ \rm \implies \: {3}^{x} = \sqrt{3 \times 3 \times 3 \times 3 \times 3} \\ \\ \implies \: \rm {3}^{x} = 3 \times 3 \sqrt{3} \\ \\ \implies \rm\: {3}^{x} = {3}^{2} \times {3}^{ \frac{1}{2} } \\ \\ \implies \: \rm {3}^{x} = {3}^{2 + \frac{1}{2} } = {3}^{ \frac{5}{2} } \\ \\ \rm{comparing \: both \: powers} \\ \\ \rm \implies \: \boxed{x = \frac \pink{5} \pink{2} }$

Answer 2

Step-by-step explanation:

Refer to the attachment......

Hope it helps u....