Question

loga(a+b)²=2+loga(1+2b/a +b²/a²)

Answer 1

Answer:

$log_{a}( {a + b})^{2} = log_{a}( {a}^{2} + 2ab + {b}^{2} )$

$= log_{a}( {a}^{2} ) . log_{a}(2) . log_{a}(a) . log_{b}(a) . log_{a}( {b}^{2} ) \\ \\ \\ = 2 log_{a}(a) . log_{a}(2).1. log_{a}(b) .2 log_{a}(b) \\ \\ \\ = 2 log_{a}(2) . log_{a}(b) (1 \times 2) \\ \\ \\ = 2 log_{a}(2) .2 log_{a}(b) \\ \\ \\ = 2 log_{a}(2) \times \frac{1}{2 log_{b}(a) }$

$= \frac{ log_{a}(2) }{ log_{b}(a) }$