Question

I need to evaluate this log, i'm honestly not sure how to do one like this, even though i can do one without the fractions.

Answer 1

- 5

Explanation:

Using the law of logarithms

•
`log_(b)` x = n ⇔ x =
`b^(n)`

let
`log_(3)`
`(1)/(243)` = n, then

`(1)/(243)` =
`3^(n)`

note that 243 =
`3^(5)`, thus

`3^(-5)` =
`3^(n)`

the bases on both sides are equal so equate the exponents

n = - 5

`log_(3)`
`(1)/(243)` = - 5