Question

How do you solve `log_2 [2^(-13)]`?

Answer 1

`log_2 2^-13=-13`

Explanation:

`log_2 2^-13=-13*log_2 2`
`log_2 2=1`
`log_2 2^-13=-13*1`
`log_2 2^-13=-13`

Answer 2

`log_2[2^-13] = -13`

Explanation:

It is important to remember that:
`color(white)("XXX")color(red)(log_b a = c color(white)("XX") "means" color(white)("XX")b^c=a)`

If
`color(white)("XXX")color(blue)(log_2[2^(-13)]=c)`
then we are asking for what value of `color(blue)(c)` is
`color(white)("XXX")color(blue)(2^c = 2^(-13))`

Hopefully the answer is clear that
`color(white)("XXX")color(blue)(c=-13)`