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After reading this text and / or viewing the video tutorial on this topic you should be able to: explain what is meant by a logarithm. state and use the laws of logarithms. solve simple equations requiring the use of logarithms.
1.2 Logarithms We use can logarithms to solve exponential equations: The solution of ax = b is x = log a b For example, the solution of ex = 2 is x = log e 2. To find the value of this logarithm, we need to use a calculator: log e 2 = 0.6931. Note Logarithms were invented and used for solving exponential equations by the Scottish baron
Examples – Now let’s use the steps shown above to work through some examples. These examples will be a mixture of logarithmic equations containing only logarithms and logarithmic equations containing terms without logarithms. Example 1 : Solve 3 log(9x2)4 + =
8. Prove the following statements. (1) logp b x = 2log x (2) log p1 b p x = log x (3) log 4 x2 = log p x 9. Given that log2 = x, log3 = y and log7 = z, express the following expressions
Having previously defined what a logarithm is (see the notes on Functions and Graphs) we now look in more detail at the properties of these functions. The relationship between logarithms and exponentials is expressed as:
LOGARITHMS PRACTICE SIMPLIFYING EXPRESSIONS. single logarithm. log 2 7 + log 2 2. log 2 20 − log 2 4. 3log 5 2 + log 5 8. 2log 6 8 − 5log 6 2. log 10 8 + log 10 5 − log 10 0.5. log 2 14 , log 2 5 , log 5 64 , log 6 2 , log 10 80. single logarithm.
The document is a textbook on logarithms containing various examples and exercises. It includes: 1) An index listing the different sections and exercises within the textbook. 2) Multiple pages of examples and step-by-step solutions working through different types of logarithm problems and calculations.
