Question

If log 2 +1/2log a+1/2 log b =log(a+b)

Answer 1

Step-by-step explanation:

Log (a + b)/2 = 1/2 (Log a + Log b)

=> Log (a + b)/2 = 1/2 Log ab

=> Log (a + b)/2 = Log ab^(1/2)

=> (a + b)/2 = ab^(1/2)

=> (a^2 + b^2 + 2ab)/4 = ab

=> a^2 + b^2 + 2ab = 4ab

=> a^2 + b^2 - 2ab = 0

=> (a - b)^2 = 0

=> a - b = 0

=> a = b

Answer 2

Step-by-step explanation:

2

1

log9+2log6+

4

1

log81−log12

=log9

2

1

+log6

2

+log81

4

1

−log12

=log3+log36+log3−log12

=log(

12

3×36×3

)=log27=log3

3

=3log3