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AS/A Level Mathematics Exponentials and Logarithms Instructions • Use black ink or ball-point pen. • If pencil is used for diagrams/sketches/graphs it must be dark (HB or B). • Fill in the boxes at the top of this page with your name. • Answer all questions and ensure that your answers to parts of questions are clearly labelled..
Calculation Problems. Instructions. • Use black ink or ball-point pen. • Answer all questions. • Answer the questions in the spaces provided. – there may be more space than you need. rately drawn, unless otherwise indicate. • You must show all your working out. Information. • The marks for each question are shown in brackets.
Maths Genie is a free GCSE and A Level revision site. It has past papers, mark schemes and model answers to GCSE and A Level exam questions.
explain what is meant by a logarithm. state and use the laws of logarithms. solve simple equations requiring the use of logarithms. Contents. Introduction. Why do we study logarithms ? What is a logarithm ? if x = an then loga x = n. 4. Exercises. 5. The first law of logarithms. loga xy = loga x + loga y. 6. The second law of logarithms.
Simplify each of the following logarithmic expressions, giving the final answer as a single logarithm. a) log 7 log 22 2+ b) log 20 log 42 2− c) 3log 2 log 85 5+ d) 2log 8 5log 26 6− e) log 8 log 5 log 0.510 10 10+ − log 142, log 52, log 645, log 26, log 8010
ogarithmic Equations EFMany mathematical models of real-life situations use ex. onentials and logarithms. It is important to become familiar with using the laws of logarithm. EXAMPLES. Solve log a 13 + log a x = log 273 for a x > 0 . log a 13 + log a x = log a 273 log a 13 x = log a 273. a x =. = 21.
593 Solve a hidden quadratic involving exponentials (with log solutions). Exponentials & Logarithms Key Skills Section (for selecting more than one) Further Practice
