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This topic introduces logarithms and exponential equations. Logarithms are used to solve exponential equations, and so are used along with exponential functions when modelling growth and decay. The logarithmic function is an important mathematical function and you will meet it again if you study calculus.
When asked to solve a logarithmic equation such as or the first thing we need to decide is how to solve the problem. Some logarithmic problems are solved by simply dropping the logarithms while others are solved by rewriting the logarithmic problem in exponential form.
•explain what is meant by a logarithm •state and use the laws of logarithms •solve simple equations requiring the use of logarithms. Contents 1. Introduction 2 2. Why do we study logarithms ? 2 3. What is a logarithm ? if x = an then log a x = n 3 4. Exercises 4 5. The first law of logarithms log a xy = log a x+log a y 4 6. The second ...
Solve the following logarithmic equations. 8. Prove the following statements. 9. Given that log 2 = x, log 3 = y and log 7 = z, express the following expressions in terms of x, y, and z. 10. Solve the following equations. 11. Draw the graph of each of the following logarithmic functions, and analyze each of them completely. 12.
We then use the rules of logarithms to simplify the expression. First use log(ab) = log a + log b We can now use log a k = k log a to get rid of the powers. Expand the brackets and collect the terms containing x on one side. Use the rules of logarithms to write the solution in the correct form: logl og log logl og log ab l b ab l a b b = b ...
logarithms. It is important to become familiar with using the laws of logarithms to help solve equations. EXAMPLES . 1. Solve log 13 log log 273. a aa += x. for . x >0. log 13 log log 273 log 13 log 273 13 273 (since log log ) 21. a aa aa. aa. x x x x y xy x += = = =⇔= = 2. Solve log 4 3 log 2 3 1. 11 ( ) xx +− −= 11 ( ) for . x > 32 ...
Worksheet 2:7 Logarithms and Exponentials Section 1 Logarithms The mathematics of logarithms and exponentials occurs naturally in many branches of science. It is very important in solving problems related to growth and decay. The growth and decay may be that of a plant or a population, a crystalline structure or money in the bank. Therefore
