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\\\\`