By Alex Bellos

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A real number. example log 2, log 3, log 5 etc. are all irrational 10 10 10 numbers. Answer: Also, log10 (1) is not a real number. The main message: if the base is positive the logarithm of a negative number cannot be a real number. com 1. All laws and rules of addition, multiplication and taking to integer power are first introduced for whole numbers and can be verified 45 (not proved) by substitution of whole numbers. It is then postulated (declared) that they extend to wider and wider number sets.

Using the Decision Tree for Solving Equations with One Term Containing the Unkown we can find the speed v. 5 A historical note “Al-Khwarizmi (Mohammad ebne Mūsā Khwārazmī was a Persian mathematician, astronomer, astrologer and geographer. He was born around 780 in Khwārizm, then part of the Persian Empire (now Khiva, Uzbekistan) and died around 850. He worked most of his life as a scholar in the House of Wisdom in Baghdad. His Algebra was the first book on the systematic solution of linear and quadratic equations.

J)Evaluate without a calculator: 3 125 j) 3 64 125 i) a) log10 2  log10 5 3 125 j) 4. b) Evaluate without calculator: log10 200  log10aa2calculator: 4. Evaluate without a) log 2 log 5  10a2 10 5 c) log log10 10000  log10 4. Evaluate a) without calculator: 10 4. 1 Graphical representation of real functions of one real variable In the last lecture we gave a diagrammatical representation of a function, ' I 5 Each particular real function of a real variable can also be visualised using a more specific, graphical, representation.

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