Question

What is `log_3 243`?

Answer 1

`log_3 243 = 5`

Explanation:

Let `x = log_3 243`

`:. 3^x = 243 = 3^5`

Equating indices`-> x=5`

Answer 2

`5`

Explanation:

We can rewrite `243` as `3^5`. We now have

`log_3 3^5`

We can now cancel the base-`3`s to get

`log_cancel3 cancel3^5=>5`

We can check this by confirming that `3^5=243`.

`3^5=9*9*3=81*3=243`

We do indeed get `5`.

Hope this helps!

Answer 3

`color(green)(log_3 243 = 5`

Explanation:

![https://mathsmethods.com.au/vce-maths-methods-lessons-cheatsheets/vce-maths-methods-logarithm-laws/]()

`log_3 243 = log_3 (3^5)`

`color(crimson)("Applying rule "log_a (m^p) = p log_a m`

`=> 5 log_3 3`

`color(maroon)("Applying rule "log_a a = 1`

`color(green)(=> 5`