Logarithms Introduction KUS objectives BAT write numbers and

Logarithms Introduction • KUS objectives BAT write numbers and expressions as logarithms Starter: sketch these graphs Check your answers on graph software

Notes on Logarithm function: A logarithm (log for short) is an index. To see this, consider the result 102 = 100 You can write this using log notation as log 10100 = 2 The number 10 is called the base of the logarithm. Similarly, 23 = 8 can be written as log 28 = 3 In this case the base is 2

WB 6 abcd Understanding logarithm functions Find the value of: What power do I raise 3 to, to get 81 ? X What power do I raise 10 to, to get 100 ? What power do I raise 7 to, to get 49 ? You can do all these on a calculator but practising helps you see what’s going on here

WB 6 efgh Understanding logarithm functions Find the value of: What power do I raise 0. 4 to, to get 4 ? X What power do I raise 10 to, to get 100 ? What power do I raise 7 to, to get 49 ? You can do all these on a calculator but practising helps you see what’s going on here

X a) What power do I raise 8 to, to get 64 ?

WB 8 Writing expressions as Logarithms ‘a’ is known as the ‘base’ of the logarithm… Effectively, the 2 stays as the ‘first’ number… The 32 and the 5 ‘switch positions’

WB 9: Evaluate the following. Check with your calculator a) log 464 b) log 101000000 c) log 1/21/8 d) logx 27 = 3 e) log 1001 f) log 81/64 g) log 22 h) log 381 X

WB 10: Choose a number from the box for the base of each of these logarithms Check with your calculator a) log. . . 16 = 2 b) log. . . 64 = 3 4 0 c) log. . . 25 = 2 5 6 d) log. . . 1 = 0 1 8 e) log. . . 1/9 = -2 3 9 f) log. . . 100 = 2 10 16 g) log. . . 1/2 = -1 2 X