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

1 Answer
May 14, 2016

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)|)))