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C2 - Chapter 3 - Exponentials and Logarithms

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by

Mr Scott

on 12 March 2015

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Transcript of C2 - Chapter 3 - Exponentials and Logarithms

buy milk
pick up kids
with
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?
try Exercise 3D
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"
Full transcript