Question

how to prove the question above​

Answer 1

Answer:

$3log(a + b) = log(a + b) + 2loga + log \: (1 + \frac{2b}{a} + \frac{ {b}^{2} }{ {a}^{2} } ) \\ rhs = log(a + b) + 2loga + log \: (1 + \frac{2b}{a} + \frac{ {b}^{2} }{ {a}^{2} } ) \: \\ = log(a + b) + loga ^{2} + log \: ( \frac{ {a}^{2} + 2ab + {b}^{2} }{ {a}^{2} } ) \\ = log(a + b) + loga ^{2} + log \: \frac{(a + b) ^{2} }{ {a}^{2} } \\ = log \: \{(a + b) \times {a}^{2} \times \frac{(a + b) ^{2} }{ {a}^{2} } \} \\ = log \: \{(a + b) \times (a + b) ^{2} \} \\ = log(a + b)^{3} \\ = 3 \: log \: (a + b) \\ = lhs \\ thus \: proved. \\ \\ please \: mark \: it \: as \: brainliest.$