Question

If (x+y)^2=125xy,show that, 2 log (x+y) = 3 log 5+log x+ log y​

Answer 1

Formulas used :

$loga^ x = x \ log a$

$logab = log a + logb$

Steps :

$(x+y)^2 = 125xy\\\\log(x+y)^2 = log(125xy)\\\\2log(x+y) = log 125 + log x + log y\\\\2log(x+y) = log 5^3+ log x + log y\\\\2log(x+y) = 3 log 5 + log x + log y$