Question

How do you solve `y = log^3(78.5)`?

Answer 1

`y=6.80358827392`

Explanation:

There is no way to simplify this, other than writing this as `log(78.5)` multiplied by itself `3` times.

`y=log^3(78.5)=log(78.5)xxlog(78.5)xxlog(78.5)`

Note that this is different than the other logarithm rules:

• `log(a^b)=bxxlog(a)`

`" "`This would apply if the question were `log(78.5^3)`.

• `log(a)+log(b)=log(ab)`

`" "`This would apply if the question were `log(78.5)+log(78.5)+log(78.5)`.

However, the only way to find this is the use a calculator:

`y=log(78.5)xxlog(78.5)xxlog(78.5)=color(blue)(6.80358827392`