Question

if x²+y²=25xy,then 2 log (x+y)=?​

Answer 1

Answer:

x

2

+y

2

=25xy....(1)

L.H.S=2log(x+y)

=log(x+y)

2

=log(x

2

+y

2

+2xy)

=log(25xy+2xy) [ from (1)]

=log(27xy)

=log(3

3

xy)

=log3

3

+logx+logy

=3log3+logx+logy

=R.H.S

Answer 2

Step-by-step explanation:

Given :-

x²+y² = 25 xy

To find :-

Find the value of 2 log (x+y) ?

Solution :-

Given that

x²+y² = 25 xy

On adding 2xy both sides then

=> x²+y²+2xy = 25xy+2xy

=> x²+2xy+y² = 27xy

=> (x+y)² = 27 xy

On taking logarithms both sides then

=> log (x+y)² = log 27xy

=> 2 log (x+y) = log 27xy

Since log a^m = m log a

We know that

log ab = log a + log b

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

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

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

Answer:-

The value of 2 log (x+y) is 3 log 3 +log x + log y

Used formulae:-

→log ab = log a + log b

→ log a^m = m log a

→ (a+b)² = a²+2ab + b²