Laws of Logarithms KUS objectives BAT know and

Laws of Logarithms • KUS objectives BAT know and apply the laws of logarithms to numbers and expressions Starter: find x if

Laws of logarithms Proof of the first rule: You do not need to know proofs of these rules, but you will need to learn and use them: Suppose that; and (The Multiplication law) (The Division law) (The Power law) ‘a must be raised to the power (b+c) to get xy’

WB 11 abc Write each of these as a single logarithm: 1) 2) 3)

WB 11 d Write each of these as a single logarithm: 4) Alternatively, using rule 4

Practice: Express each of these as a single logarithm (log is log 10) a). log 3 + log 5 b). log 27 – log 9 c). 3 log 2 + log 4 – log 8

WB 12 Write the following as a single logarithm. a). log 2 4 + log 2 3 Write each logarithm as the difference between two logarithms. a). log 5 (7/2) b). log 3 (4/3) Simplify the following. a). log 3 34 b). log 2 32 Simplify the following. a). 4 log 2 3 + 2 log 2 5 b). log 3 45 - log 3 5

Challenge work in pairs Choose four integers between 1 and 8 inclusive, called a, b, c, d Work these out or simplify into as few terms as possible

WB 13 ab Using algebra Write in terms of logax, logay and logaz 1) 2)

WB 13 cd continued 3) 4) =1

WB 14 Express each of these in terms of log a, log b, log c. a) log (1/a 2) b) log (ab/c) c). log √(a/bc 2) d) log (ab 3 c 2) e) log (2 ab 2/c) f) 2 log (a√ 3/b√c) g) 2 log x – 3 log y + 2 log xy h) 3

WB 15 exam Q

WB 16 exam Q

Summary: Laws of logarithms You should learn these laws of logarithms To prove these laws, let x = loga. P and y = loga. Q. Then ax = P and ay = Q. . . Note: These three laws are true for any base. If you are using logs to the same base then you usually leave the base out and simply write log x. You must also remember :

KUS objectives BAT know and apply the laws of logarithms to numbers and expressions self-assess One thing learned is – One thing to improve is –

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