1. C2: Solving Equations with Logarithms Learning Objective: to be able to solve equations of the form a x = b

2. Remember the Laws of Logarithms: log a (1/x) = -log a x n log a x = log a x n log a x + log a y = log a ( xy ) y = log a x  a y = x

3. Solving equations of the form a x = b We can use logarithms to solve equations of the form a x = b. For example: Find x to 3 significant figures if 5 2 x = 30. We can solve this by taking logs of both sides: log 5 2 x = log 30 2 x log 5 = log 30 Using a calculator: x = 1.06 (to 3 s.f.)

4. Task 1 : Worksheet questions 1 - 6

5. Solving equations of the form a x = b Find x to 3 significant figures if 4 3 x +1 = 7 x +2. Taking logs of both sides:

6. Task 2 : Worksheet questions 6 - 12

7. Solving equations of the form a x = b Solve 3 2 x –5(3 x ) + 4 = 0 to 3 significant figures. If we let y = 3 x we can write the equation as: So: If 3 x = 1 then x = 0. Now, solving 3 x = 4 by taking logs of both sides:

8. Task 3 : Worksheet questions 13 - 20