Question

Express 1÷2 log (x+y) - 1÷2 log (x-y)
as a
single
logarithm​

Answer 1

Step-by-step explanation:

(\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

) .

#Learn more

The value of log3 9 – log5 625 + log7 343 is