Nursing - Medium Difficulty Story Problem

This problem uses the half life formula, Half life formula D=D0*(1/2)^(t/h). Since D0 is the initial dose of the drug, D0 = 500 mg. The half life is h, so h = 6. Since there must be at least 120 mg of drug in the patient, the level of the drug we are solving for is 120mg. This gives us the equation
125=500*(1/2)^(t/6)

We can now solve for t. Here is how we solve this equation.
ResultMathematics Operation
125/500=(1/2)^(t/6)Divide both sides by 500.
0.25=(1/2)^(t/6)Simplify faction on the left side.
0.25=(1/2)^(t/6) implies log<SUB>1/2</SUB>0.25 = t/6 Since the variable is in the exponent, apply the definition of a logarithm: a^b=c implies log base a of c = b.
2=t/6Since log<SUB>1/2</SUB>0.25 = 2, substitute 2 in for the logarithmic expression.
2*6=tMultiply both sides by 6.
12=tSimplify right hand side.