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Logarithmic and trigonometric equations

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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Solution Summary

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.