Question

How do you solve for t in `44=2,500times0.5^(t/5.95)`?

Answer 1

`t~~34.68`

Explanation:

Given,

`44=2500*0.5^(t/5.95)`

Divide both sides by `2500`.

`44/2500=0.5^(t/5.95)`

Take the logarithm of both sides since the bases are not the same.

`log(44/2500)=log(0.5^(t/5.95))`

Using the logarithmic property, `log_color(purple)b(color(blue)x^color(red)y)=color(red)y*log_color(purple)b(color(blue)x)`, the equation becomes,

`log(44/2500)=(t/5.95)log(0.5)`

`log(44/2500)=log(0.5)/5.95*t`

Solve for `t`.

`t=log(44/2500)/(log(0.5)/5.95)`

`t=(5.95log(44/2500))/(log(0.5))`

`color(green)(|bar(ul(color(white)(a/a)color(black)(t~~34.68)color(white)(a/a)|)))`