Question

Log(b-a)+log(a+b)-log(b2-a2)=

Answer 1

Answer:-

$\sf \log(b - a) + \log(a + b) - \log( {b}^{2} - {a}^{2} )$

$\sf = \log \big( \frac{(b - a)(b + a)}{( {b}^{2} - {a}^{2} )} \big)$

$\sf = \log( \frac{ {b}^{2} - {a}^{2} }{ {b}^{2} - {a}^{2} } )$

$\sf = \log(1)$

$\sf = 0$

Hence, the required answer is 0.

Answer 2

Answer:

log(b−a)+log(a+b)−log(b

2

−a

2

)

\sf = \log \big( \frac{(b - a)(b + a)}{( {b}^{2} - {a}^{2} )} \big)=log(

(b

2

−a

2

)

(b−a)(b+a)

)

\sf = \log( \frac{ {b}^{2} - {a}^{2} }{ {b}^{2} - {a}^{2} } )=log(

b

2

−a

2

b

2

−a

2

)

\sf = \log(1)=log(1)

\sf = 0=0

Hence, the required answer is 0.

hope it helps