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Starter Simplify 1) 10 32 x ÷ 4x 4 = 2) (16 x 4 ) 0.5 = 3) 3 27a12 = Write these in surd form 4) x 2 7 5) 2 3 (27x) 2 5 6) x 9) 83 x Write these in index form 7) 3 x10 8) 4 625 x12 HW Theta pg 32 & 33 Done? 4 Expressing numbers as powers of the same base 9 5 3 2 5 3 10 Use the rule x a b 95 2 27 so 5 2 Theta Ex 8.06 x ab to rewrite the powers with a common base Express the following as a power of 3 Express the following as a power of 9 1) 27 = 4) 6561 = 2) 243 = 1 5) 81 Solve these equations 7) 3 x 243 Simplify 64x n 3n 10) 4 5n 2 2 x 8x 4 8) 11) 2 6n 2 x n 1 9) 3 x 3 9 x 1 16 m 1 3x 4 m m 1 m 3 2 9 x m 12) 3) 6) 1 81 1 3 . Logarithms: What do you notice? . Ex 9.01 Write the equivalent index statement 1) Log39 = 2 32 = 9 2) Log416 = 2 42 = 16 3) Log5125 = 3 53 = 125 4) Log99 = 1 91 = 9 5) Log101000 = 3 103 = 1000 6) Log3243 = 5 35 = 243 Find the value of ‘w’ in each of: 7) Log3w = 4 w = 81 8) Log6w = 5 w = 7776 9) Log2256 = w w=8 10) Log32187 = w w=7 11) Logw27 = 3 w=3 12) Logw729 = 3 w=9 Logarithms Logarithms were invented by John Napier in 1614. They were initially used to solve complex multiplication and division problems. Logs get at the power… 24 = 16 is equivalent to Index equation log2 16 4 Log equation log2 16 4 means “what is the power on 2 which gives a result of 16? Answer = 4” Said as “Log base 2 of 16 is 4” or “Log of 16 to the base 2” The most common logs used are to the base 10 and e (e = 2.71828182845905…) On the calculator these are the Log (log base 10) and Ln (log base e) functions 10 3 1000 Log10 1000 3 2 5 32 Log2 32 5 Logs Skills Skills: Convert between index equation and log equation 1) 28 = 256 2) log3 243 5 4) log1 0 10000 6) logx 15625 6 Calculate logs 3) log2 1024 Solve log equations 5) log4 x 5 HW Theta pg 34 & 35 Theta Ex 9.01