Question

3) Express 1/2 log(x+y) = 1/2 log(x+y) as single logoritham.​

Answer 1

Answer:

The required expression is \log (\dfrac{\sqrt{x+y}}{\sqrt{x-y}})log(

x−y

x+y

) .

Step-by-step explanation:

The given expression is

\dfrac{1}{2}\log (x+y)-\dfrac{1}{2}\log (x-y)

2

1

log(x+y)−

2

1

log(x−y)

We need to expression the given problem as single logarithm.

Using properties of logarithm we get

\log (x+y)^{\frac{1}{2}}-\log (x-y)^{\frac{1}{2}}log(x+y)

2

1

−log(x−y)

2

1

[\because \log a^b=b\log a][∵loga

b

=bloga]

\log \sqrt{(x+y)}-\log \sqrt{(x-y)}log

(x+y)

−log

(x−y)

\log (\dfrac{\sqrt{x+y}}{\sqrt{x-y}})log(

x−y

x+y

) [\because \log (\dfrac{a}{b})=\log a-\log b][∵log(

b

a

)=loga−logb]

Therefore, the required expression is \log (\dfrac{\sqrt{x+y}}{\sqrt{x-y}})log(

x−y x+y) .