Question

Which expressions are equivalent to the one below?
log 2- log 8

Answer 1

A.
`\log (2)+\log ((1)/(8))`

B.
`log ((1)/(4))`

Explanation:

Given expression:

`\log 2-\log 8`

Using properties of logarithm we can write the expression in various equivalent forms:

1) Using quotient rule
`[\log a-\log b=log (a)/(b)]` :

`\log 2-\log 8`

⇒
`log (2)/(8)]`

Reducing
`(2)/(8)` to simple fraction by dividing numerator and denominator by their greatest common factor.

⇒
`log (2/ 2)/(8/ 2)]`

⇒
`log (1)/(4)]`

2) Plugging in
`\log 1` in the expression as
`\log 1=0`

⇒
`\log 2+\log 1-\log 8`

Using quotient rule again
`[\log a-\log b=log (a)/(b)]`

⇒
`\log 2+\log (1)/(8)`