Question

x²+x³=6xy then prove that 2log(x+y)=logx+logy+ 2log3​

Answer 1

Required Answer:-

Correct Question:

• If x² + y² = 6xy, then prove that 2 ㏒(x + y) = ㏒(x) + ㏒(y) + 3 ㏒(2)

Proof:

Given that,

→ x² + y² = 6xy

Adding 2xy to both sides, we get,

→ x² + 2xy + y² = 8xy

Using identity, (a + b)² = a² + 2ab + b², we get,

→ (x + y)² = 8xy

Taking ㏒ on both sides, we get,

→ ㏒(x + y)² = ㏒(8xy)

We know that,

→ ㏒ₓyⁿ = n ㏒ₓy

→ ㏒(abc...) = ㏒(a) + ㏒(b) + ㏒(c) +...

So,

→ 2 ㏒(x + y) = ㏒(8) + ㏒(x) + ㏒(y)

→ 2 ㏒(x + y) = ㏒(x) + ㏒(y) + ㏒(2)³

→ 2 ㏒(x + y) = ㏒(x) + ㏒(y) + 3 ㏒(2)

Hence, Proved.

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