Question

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

log 2 - log 6

Answer 1

There are no correct expressions listed.

Log(2) - log(6) is equivalent to

log(1/3)
or
-log(3)
or
-0.47712...
or
any one of a bunch of others.

Answer 2

Given the expression: log 2 -log 6

Use the logarithmic rule :

`\log((m)/(n)) = \log m - \log n`

`\log x^n = n\log x`

Use the above rule to solve the expression:

`\log 2 -\log 6 = \log (2)/(6) = \log (1)/(3)` [∴
`\log((m)/(n)) = \log m - \log n` ]

or

`\log 2 -\log 6 =\log 2+ \log 6^(-1) = \log 2 + \log (1)/(6)` [∴
`\log x^n = n\log x` ]

or

value of : log 2 -log 6 = 0.30102999566 - 0.77815125038 = -0.47712125472