Question

x2+y2=25x then prove that 2log (x+y)=3 log 3+log x +log y​

Answer 1

Answer:

x²+y²=25xy

adding 2xy on both sides

x²+y²+2xy=27xy

[x+y]²=27xy

taking log on both sides  

log[x+y]²=log27xy

2log[x+y]=log3³+log x+log y

2 log[x+y]=3log3+logx+logy

Step-by-step explanation:

Answer 2

Required Answer:-

Given:

• x² + y² = 25x

To prove:

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

Proof:

We have,

➡ x² + y² = 25x

Adding 2xy on both sides, we get,

➡ x² + 2xy + y² = 27xy

➡ (x + y)² = 27xy

Taking Log on both the sides, we get,

➡ log(x + y)² = log(27xy)

➡ 2log(x + y) = log(27) + log(x) + log(y)

➡ 2log(x + y) = log(3³) + log(x) + log(y)

➡ 2log(x + y) = 3log(3) + log(x) + log(y) [Hence Proved]

Formula Used:

• log(x)ⁿ = n log(x)
• log(ab) = log(a) + log(b)