Question

Expand the logarithmic expression: log3 d/12

The answer should not be a number!(it should be a different expression).

Answer 1

log(base 3)(d/12) = log(base 3)d - log(base 3)12

Explanation:

Answer 2

Expanded form:
`\Rightarrow \log_3d-2\log_32-1`

Explanation:

Given:
`\log_3(d)/(12)`

Subtraction property of log: log a/b = log a - log b

Addition property of log: log(ab) = log a+ log b

`\log_aa=1`

`\log_ab^m=m\log_ab`

`\log_3(d)/(12)=\log_3d-\log_312` (Subtraction property )

`\Rightarrow \log_3d-\log_3(4* 3)`

`\Rightarrow \log_3d-(\log_34+\log_33)` (Addition Property)

`\Rightarrow \log_3d-\log_34-\log_33` (Distributive property)

`\Rightarrow \log_3d-\log_34-1` (
`\log_aa=1`)

`\Rightarrow \log_3d-2\log_32-1`

The expanded form of
`\log_3(d)/(12)` is

`\Rightarrow \log_3d-2\log_32-1`

Hence, Expanded form:
`\Rightarrow \log_3d-2\log_32-1`