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

##### 1 Answer

May 14, 2016

#### Explanation:

Given,

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

Divide both sides by

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

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

Solve for

#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)|)))#