Question

Heya....^_^

✍ here's the question ⬇


↪
$log_{5}((a + b )\div 3) = (log_{5}(a) + log_{5}(b)) \div 2$
Then ,

$(a {}^{4} + {b}^{4} ) \div {a}^{2} {b}^{2} =$
?


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Require proper explanation

Tysm ☺

Answer 1

Solution :

$log_{5} \left ( \frac{a + b}{3} \right) = \frac{ log_{5}(a) + log_{5}(b) }{2} \\ \\ 2log_{5} \left ( \frac{a + b}{3} \right) = { log_{5}(a) + log_{5}(b) } \\ \\ log_{5} {\left ( \frac{a + b}{3} \right) }^{2} = log_{5}(ab) \\ \\ \Rightarrow \: \: \: {\left ( \frac{a + b}{3} \right) }^{2} = ab \\ \\ \Rightarrow \: \: \: \frac{ {a}^{2} + {b}^{2} + 2ab}{9} = ab \\ \\ \Rightarrow \: \: \: {a}^{2} + {b}^{2} + 2ab = 9ab \\ \\ \Rightarrow \: \: \: {a}^{2} + {b}^{2} = 7ab \\ \\ \text{Squaring both sides, We get}\\ \\ {( {a}^{2} + {b}^{2} )}^{2} = {(7ab)}^{2} \\ \\ \Rightarrow \: \: \:{a}^{4} + {b}^{4} + 2 {a}^{2} {b}^{2} = 49 {a}^{2} {b}^{2} \\ \\ \Rightarrow \: \: \: {a}^{4} + {b}^{4} = 47 {a}^{2} {b}^{2} \\ \\ \Rightarrow \: \: \: \boxed{ \frac{ {a}^{4} + {b}^{4} }{ {a}^{2} {b}^{2} } = 47}$

Answer 2

Answer:

Its your answers................