Question

If x2 + 4y2 = 12xy, then log (x + 2y) is equal to​

Answer 1

Question :- If x² + 4y² = 12xy, then log (x + 2y) is equal to ?

Solution :-

→ x² + 4y² = 12xy

Adding 4xy both sides we get,

→ x² + 4y² + 4xy = 12xy + 4xy

→ (x)² + (2y)² + 2 * x * (2y) = 16xy

Comparing LHS with a² + b² + 2ab = (a + b)² we get,

→ (x + 2y)² = (2)⁴xy

Taking log both sides now,

→ log{(x + 2y)²} = log{2⁴xy}

Now in LHS, using log(a^b) = b*log(a) and in RHS, using log(abc) = log(a) + log(b) + log(c) , we get,

→ 2 * log(x + 2y) = log(2⁴) + log(x) + log(y)

→ 2 * log(x + 2y) = 4log(2) + log(x) + log(y)

Dividing by 2 both sides now, we get,

→ log(x + 2y) = (1/2) [ 4log(2) + log(x) + log(y) ] (Ans.)

Learn more :-

if X2+Y2=18xy then prove that 2log(x-y)=4log2+logx+log y

step by step please

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