Question

How do you expand `log (10/y)`?

Answer 1

`log10-logy`

Explanation:

The second law of logs says tha `logcolor(red)(x)-logcolor(blue)(y)` can be simplified to `log(color(red)(x)/color(blue)(y))`. The only requirement for this to work is that both `log`s must have the same bases.

For our problem of `log(10/y)`, we have to expand the expression. We need make sure that we end up with two `log`s with the same bases.

The first step is also the last step: take the numerator, and make that the first part of the expression, and make the denominator the second part. What I mean is this: `log(color(red)(10)/color(blue)(y))` becomes `logcolor(red)(10) color(orange)(-) logcolor(blue)(y)`. The `color(orange)(-)` is very important, because that is what differentiates division from multiplication.