Posted by **Ku** on Sunday, June 23, 2013 at 1:44am.

Solve the exponential equation algebraically

5^(-t/2) = 0.20

- Precal -
**MathMate**, Sunday, June 23, 2013 at 5:30am
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

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