Precal
posted by Ku .
Solve the exponential equation algebraically
5^(t/2) = 0.20

5^(t/2)=0.20
take log on both sides,
(t/2)log(5)=log(0.20)
solve for t
t/2 = log(0.20)/log(5)
t=2log(0.20)/log(5)...isolate t
=log(1/0.04)/log(5)...absorb 2 into log(0.2)
=log(25)/log(5)... evaluate reciprocal
=2... laws of logarithm, 25=5²