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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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The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

The log function has the following properties:


Remember that means that and that if then hence:

However, note that and generally it is not ...

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.