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8303233-66-Maths-4-Chemists-21

# 8303233-66-Maths-4-Chemists-21 - Chem Factsheet...

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Maths for Chemists 2 C hem F actsheet www.curriculumpress.co.uk Number 66 1 This Factsheet covers logarithms and their use in Chemistry. What are logarithms? Logarithms are closely related to powers, so before continuing, make sure you know and understand the power facts in the box (right). To see how logarithms work, consider the following examples: 100 = 10 2 log 10 100 = 2 0.001 = 10 -3 log 10 0.001 = -3 So when we say "what is log 10 1000?", we are asking "What power must I raise 10 to, to get the answer 1000?" The answer is 3 - so log 10 1000 = 3 Although you can have logarithms to different bases, in Chemistry we will only be looking at logarithms to the base 10 (log 10 ). To save time, we'll just write "log" when we mean "log 10 " Calculating logs It's easy to work out logs for numbers that are exact powers of 10 and it's worth being able to do so mentally to save time in the exam and guard against calculator error. But logs for other numbers have to be worked out on your calculator. The button for finding log to the base 10 may be labelled: LOG LOG 10 LG Note: do NOT use the button labelled ln or log e . This gives you logarithms to a different base - and hence the wrong answers! Some calculators require you to put the number in first, then press the log button - in others, you press the log button first, then the number. Check which yours is by finding log100 (the answer should be 2). Exam Hint : You should never get a negative number from either of the above methods. It's impossible to find the log of a negative number - if you think you have, then you've probably pressed LOG not INV LOG. Powers Raising a number to a positive power means multiplying it by itself that number of times - eg 10 6 = 10 × 10 × 10 × 10 × 10 × 10 Special cases: any number to the power 1 is the number itself; any number to the 0 gives 1 - eg 2 1 = 2 3 0 = 1 Negative powers of a number are one over the corresponding postive power - eg You can also have powers that are decimals - eg 10 2.156 You find powers on your calculator using the button marked x y (or y x ) - eg to find 10 2.156 , type in 10, then x y , then 2.156 (check - the answer should be 143.2) When doing work on logarithms in Chemistry, you mainly deal with powers of 10 - so, a few facts about them: Positive powers of 10 are easy to recognise - just count the zeroes! eg 10 1 = 10 10 3 = 1000 Negative powers of 10 are easy to recognise as decimals - just count the decimal places! eg 10 -1 = 0.1 10 -4 = 0.0001 Positive powers are larger than 1; negative powers smaller than 1 3 3 1 1 1 10 10 10 10 1000 10 = = = × × Finding the number that has a particular log There are two ways of doing this on your calculator: Use the x y (or y x ) button to find 10 to the power of the number eg: logx = 0.123. To find x, enter 10 x y 0.123 Use the INV or 2ND or SHIFT button, together with the LOG button On some calculators you have to press INV LOG first, then the number; on others you press the number then INV LOG. Check which yours is by using this method to solve logx = -1.23 (ans 0.0589) If a number has a whole-number log (eg logx = -4 or logy = 3) then you can find the number without a calculator: logx = -4 so x = 10 -4 = 0.0001

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8303233-66-Maths-4-Chemists-21 - Chem Factsheet...

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