Logarithms Laws (Unity) loga a = 1 Example: log88 = log8 81 y = 81 a = 8 = 1 x = x y = ax 81 = 8x x = 1

Logarithms Laws (Multiplication) loga(xy) = logax + logay Example: log327 + log33 = log3 (27 x 3) y = 34 a = 3 = log3 81 x = x = log3 34 y = ax = 4 34 = 3x x = 4

Logarithms Laws (Division) loga(x/y) = logax - logay Example: log327 - log33 = log3 (27 ÷ 3) y = 32 a = 3 = log3 9 x = x = log3 32 y = ax = 2 32 = 3x x = 2

Logarithms Laws (Powers) loga xn = n logax Example: log381 = log3 34 y = 31 a = 3 = 4 log33 x = x = 4 x 1 y = ax = 4 31 = 3x x = 1

Logarithms Laws (Examples) Given log53 = 0.68 and log54 = 0.86 1) log512 2) log50.75 = log5(3x4) = log5(3÷4) = log53 + log54 = log53 - log54 = 0.68 + 0.86 = 0.68 - 0.86 = 1.54 = -0.18

Logarithms Laws (Examples) Given log53 = 0.68 and log54 = 0.86 3) log59 4) log520 = log5(3x3) = log5(5x4) = log53 + log53 = log55 + log54 Exercise 4.5 (page 143) = 0.68 + 0.68 = 1 + 0.86 = 1.36 = 1.86