Question

How do you write `9^(3/2) = 27` in log form?

Answer 1

`log_{9}(27)=3/2`

Explanation:

For `b>0`, `b!=1` and `y>0`, the symbol `x=log_{b}(y)` represents the unique real number such that `b^{x}=y` (it's the unique solution of that equation).

Since `x=3/2` is the unique solution of the equation `9^{x}=27`, it follows that `log_{9}(27)=3/2`.