Question

How do you evaluate `log 0.01`?

Answer 1

I found `-2` if the log is in base `10`.

Explanation:

I would imagine the log base being `10`
so we write:
`log_(10)(0.01)=x`
we use the definition of log to write:
`10^x=0.01`
but `0.01` can be written as: `10^-2` (corresponding to `1/100`).
so we get:
`10^x=10^-2`
to be equal we need that:
`x=-2`
so:
`log_(10)(0.01)=-2`

Answer 2

`log 0.01=-2`

Explanation:

`log 0.01`
`=log (1/100)`
`=log(1/10^2)`
`=log10^-2`-> use property `1/x^n = x^-n`
`-2log10`->use property `log_b x^n=n*log_bx`
`= -2(1)`->log 10 is 1
`=-2`

Answer 3

`-2`

Explanation:

`\log0.01`

`=\log(1/100)`

`=\log(10^{-2})`

`=-2\log10`

`=-2\cdot 1`

`=-2`