pick up kids

**with**

Pete Scott

Pete Scott

**Chapter 3:**

you have a lot more formulae given to you in C2

Now lets try Exercise 3E

The Laws of Logarithms

Solving equations of the form

**Exponentials and Logarithms**

powers and stuff

What are Logarithms?

its always fun learning how to use a new button on your calculator

log n = x

means that

a = n

a

x

log x +

a

log xy =

a

log y

a

log x -

a

log y

a

log =

a

X

**_**

y

**(**

**)**

log x =

a

klog x

a

k

What did people do before calculators?

they had to use a log book.

x

a = b

a logarithm is a function and is now a new technique you can use in conjunction with your other algebraic methods

solve the equation:

x

3 = 20

x

log (3 ) = log 20

take logs to the base 10 on both sides

10

10

x

log (3) = log 20

10

10

x

log (3)

10

10

= log 20

Changing the base

rearranged this makes:

substitute m:

using the power law:

taking logs to a different base:

writing this as a power:

working in base a suppose that:

log x = m

log x = log (x) X log (a)

mlog (a) = log (x)

log (a ) = log (x)

a = x

b

a

b

b

b

b

m

b

m

a

log x =

log a

log x

**_**

a

b

b

a special case worth noting is what happens when you change

log b

to the base

b

a

give it a go

log a

log b =

1

a

**_**

b

A couple of examples

for the board:

1) Find to 3sf the value of

8

5

log x + 6log 5 = 5

2) Solve the equation

x

log 11

Keep an eye out for questions like this

tHIS IS

PREZI

read "log base a of n"