Question

Condense to a single logarithm : log 12 18+3 log 12 2

Answer 1

2 or
`\log_(12) 144`

Explanation:

I assume 12 is the base.

`\log_(12) 18 + 3 \log_(12) 2 =`

`= \log_(12) 18 + \log_(12) 2^3`

`= \log_(12) (18 * 8)`

`= \log_(12) 144`

`= \log_(12) 12^2`

`= 2\log_(12) 12`

`= 2`

The entire expression simplifies to 2, but if you need the simplest log expression, then you can use

`\log_(12) 144`