Question

If x²+y² =6y ,
Then prove that,
2log(x+y) =logx+logy+3log2 .

Answer 1

Answer:

LHS=RHS

Step-by-step explanation:

x^2+y^2 = 6xy

add both sides 2xy ..

x^2+y^2+2xy=6xy+2xy

now [(x^2+y^2+2xy=(x+y)^2]...

(x+y)^2=8xy

add log on both sides...

log(x+y)^2=log8xy

by logarithm identities ...

log(x+y)^2=2log(x+y) [LHS]

log abc= log a + log b + log c [RHS]

then,

2log(x+y) = log 8 + log x + log y

2log(x+y) = log 2^3 + log x + log y

since, log a^m =mloga

so,

2log(x+y)= log x + log y + 3log2

LHS= RHS

HENCE PROVED