Question

Check my working out please

Answer 1

\[\log_{2} \frac{ 3 }{ 25 }\sqrt{30}\]
\[\log_{2}3+-(2\log_{2} 5) + \log_{2}3^{\frac{ 1 }{ 2 }}+\log_{2}2^{\frac{ 1 }{ 2 }}+\log_{2}5^{\frac{ 1 }{ 2 }} \]

\[\log_{2}3-2\log_{2} 5 + \log_{2}3^{\frac{ 1 }{ 2 }}+\frac{ 1 }{ 2 }+\log_{2}5^{\frac{ 1 }{ 2 }} \]

Answer 2

similiar question as last time @hartnn

Answer 3

one more simplification step is possible :
for log2 3^1/2 and log2 5^1/2

Answer 4

infact 2 more steps