Question

How do you solve `428^-x = 37.5`?

Answer 1

`x\approx-0.5981626...`

Explanation:

`\color(indianred)(a^x=b)\leftrightarrow\color(olive)(\log_(a)(b)=x)`

input in values:
#\color(indianred)(428^(-x)=37.5)\leftrightarrow\color(olive) (\log_428(37.5)=-x)#
divide both sides by -1 to isolate `x`:
`\log_428(37.5)/\color(red)(-1)=(\cancel(-)x)/\cancel(\color(red)(-1))`
`-\log_428(37.5)=x`

`x\approx-0.5981626...`