Half-life of Radioactive Substance: Solve Algebraically w/Logarithms

[Z-Score]

If 3150g of a radioactive substance decays to 450g in 73 weeks, determine the half life of the substance to the nearest week. Solve algebraically using logarithms.

450=3150(x)^73
450/3150=x^73
73sqrt(450/3150)=x

Now, the only problem is the answer says it is 26 weeks. Any help is much appreciated.

 

[Tide]

You're starting with the wrong equation. Try something like

450 = 3150 \left( \frac {1}{2} \right)^{73/T}

where T is the half-life.