Question

if x power 2+y power 2=25xy then prove that 2log(x+y)=3log3+logx+logy​

Answer 1

Step-by-step explanation:

Given:-

x^2 + y^2 = 25xy

To find:-

Prove that 2log(x+y)=3log3+logx+logy

Solution:-

Given that :

x^2 + y^2 = 25xy

On adding 2xy both sides then

=> x^2 + y^2 + 2xy = 25xy + 2xy

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

(Since (a+b)^2 = a^2+2ab+b^2

Where a = x and b = y)

On taking Logarithms both sides then

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

=> log ( x + y )^2 = log (3×3×3×x×y)

=> log ( x + y )^2 = log ( 3^3 × x×y)

We know that

log ab = log a + log b

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

We know that

log a^m = m log a

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

Hence , Proved

Used formulae:-

• (a+b)^2 = a^2+2ab+b^2

• log ab = log a + log b

• log a^m = m log a