Section on using the properties of algebraic, trigonometric, logarithmic and exponential functions to solve problems.
1) Solve the following equation: log5 X + log5(X-2) = log5 X
2) The half-life of a certain radioactive element is 100days. That means that after 100 days ½ of the radioactive substance will have decayed to one half of its original amount. How long will it take to decay to ¼ of the original amount if decay equation is of the form A(t) = Ce^kt where C is the amount of substance.
3) Show on unit circle: sin(- x) = -sin x, cos(- x) = cos x, and what tan(- x) equals.
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The solution is attached ...
The solution demonstrates how to solve logarithmic equations, explains in length the concepts of radioactive decay and illustrates the relations between trigonometric functions on the unit circle.