Question

How do you simplify `[ln(1/4)]/ln2`?

Answer 1

`-2`

Explanation:

`1`. Looking at `ln(1/4)`, express `1/4` in terms of `2`.

`(ln(1/4))/ln2`

`=(ln(2^-2))/ln2`

`2`. Use the natural logarithmic property, `ln_color(purple)e(color(red)m^color(blue)n)=color(blue)n*ln_color(purple)e(color(red)m)`, to simplify the numerator.

`(-2ln2)/ln2`

`3`. `ln2` cancels each other out in the numerator and denominator.

`(-2color(red)cancelcolor(black)(ln2))/color(red)cancelcolor(black)(ln2)`

`=color(green)(|bar(ul(color(white)(a/a)-2color(white)(a/a)|)))`