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)|)))#