Find the value of y such that log2 y= –3

Find the positive value of x such that logx 64 = 2

We can simplify logs in the same way we simplify indices

loga (xy) = logax + logay

loga x = logax – logay yloga1/x = -loga x

loga xn = nlogax

logaa = 1 and loga1 = 0

Example

Write as a single log

log36 + log37

2log53 + 3log52

Note : like indices, they must have the same base!

SolvingSolving

We can solve exponential equations by using logs

Solve, 3x = 20

Solve 7x+1 = 3x+2

Solve 52x + 7(5x) – 30 = 0

Solve the equation log3(5x-1) - log3(x+1) = 1

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)

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)