Question

Which expression is equivalent to log12 (1/2/8w)

Answer 1

Answer:B

Explanation:

Answer 2

`log_(12)((1)/(2) )-(log_(12)(8 )+log_(12)(w))`.

Explanation:

The given logarithmic expression is
`log_(12)(((1)/(2) )/(8w))`.

We need to apply the quotient rule of logarithm, which is given as follows;

`log_(a)((M)/(N) )=log_(a)(M )-log_(a)(N )`.

We apply this property to obtain,

`log_(12)(((1)/(2) )/(8w))=log_(12)((1)/(2) )-log_(12)(8w )`.

We again apply the product rule which is given as;

`log_(a)({M* N)=log_(a)(M )+log_(a)(N )`.

We apply this rule to the last term to get,

`log_(12)(((1)/(2) )/(8w))=log_(12)((1)/(2) )-(log_(12)(8 )+log_(12)(w))`.

Therefore, the correct answer is B.