Question

625)
5. If x+y=11xy, then prove that 2 log(x - y) = 2log3 + logx + logy.​

Answer 1

$\huge\underline\purple{★ Question : }$

If x² +y² = 11xy, then prove that 2 log(x - y) = 2log3 + log x + log y.

$\huge\underline\purple{★ Solution : }$

➡ x² + y² = 11xy

• Add “ - 2xy ” on both sides.

➡ x² + y² - 2xy = 11xy - 2xy

• LHS in the form of " x²+ y²- 2xy = (x - y)² ".

➡ (x - y)² = 9xy

• Apply " log " on both sides.

➡ log (x - y)² = log 9xy

• [ log xⁿ = n log x ]

➡ 2 log (x - y) = log 9xy

• [ log xy = log x + log y ]

➡ 2 log (x - y) = log 9 + log x + log y

➡ 2 log (x - y) = log 3² + log x + log y

• [ log xⁿ = n log x ]

➡ 2 log (x - y) = 2 log 3 + log x + log y

➡ 2 log (x - y) = 2 log 3 + log x + log y

$\underline{\boxed{\bf{\purple{∴ Hence,\;it\;is\;proved.}}}}$

Step-by-step explanation:

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