1. Find the value of y such that
log2 y= –3
Find the positive value of x such that
logx 64 = 2

2. Logs

3. We can simplify logs in the same way we simplify indices
loga (xy) = logax + logay
loga x = logax – logay y
loga1/x = -loga x
loga xn = nlogax
logaa = 1 and loga1 = 0

4. Example Write as a single log log36 + log37 2log53 + 3log52
Note : like indices, they must have the same base!

5. Solving
We can solve exponential equations by using logs
Solve, 3x = 20

6. Example 1
Solve 7x+1 = 3x+2

7. Example 2
Solve 52x + 7(5x) – 30 = 0

8. Example 3
Solve the equation log3(5x-1) - log3(x+1) = 1

9. May 2007 qu 6
(a) Find, to 3 significant figures, the value of x for which 8x = 0.8.
(2)
(b) Solve the equation
2 log3 x – log3 7x = 1
(4)

10. Jan 08 qu 5
Given that a and b are positive constants, solve the simultaneous equations
a = 3b,
log3a + log3b = 2.
Give your answers as exact numbers.
(6)