# Precal

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Solve the exponential equation algebraically
5^(-t/2) = 0.20

• Precal -

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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