Question

Which expressions are equivalent to the one below? Check all that apply. Log2- log6

Answer 1

The expression
`\(\log(2) - \log(6)\)` is equivalent to
`\(\log\left((1)/(3)\right)\)`. Therefore, the correct option is C:
`\(\log\left((1)/(3)\right)\)`.

To find the equivalent expressions, we can use logarithmic properties. The given expression is:
`\[ \log(2) - \log(6) \]`

Using the quotient rule
`(\(\log(a) - \log(b) = \log\left((a)/(b)\right)\))`, we can combine the logarithms:
`\[ \log\left((2)/(6)\right) \]`

Now, simplify the fraction:
`\[ \log\left((1)/(3)\right) \]`

So, the equivalent expression is
`\( \log\left((1)/(3)\right) \)`.

Now, let's check the options:

A.
`\( \log 3 \)` - Not equivalent.

B.
`\( \log(2) + \log\left((1)/(6)\right) \)` - Not equivalent.

C.
`\( \log\left((1)/(3)\right) \)` - Equivalent.

D.
`\( \log(2) \)` - Not equivalent.

Therefore, the correct answer is C.
`\( \log\left((1)/(3)\right) \)`.

The complete question is:

Which expressions are equivalent to the one below? Check all that apply.

log(2) - log(6)

A. log 3

B. log(2) + log(1/6)

C. log(1/3)

D. log(2)