C2: Logarithms

1
C2 Logarithms

• Learning Objective to be able to write an
  expression in logarithmic form

2

• Logarithmic functions are the inverses of the
  exponential functions.
• The graph of a logarithmic function is the
  inverse of its exponential function (ie a
  reflection in the line yx)

3
Logarithms
Find p if p3 343.
We can solve this equation by finding the cube
root of 343
Now, consider the following equation
Find q if 3q 343.
We need to find the power of 3 that gives 343.
One way to tackle this is by trial and
improvement.
Use the xy key on your calculator to find q to 2
decimal places.
4
Logarithms
To avoid using trial and improvement we need to
define the power y to which a given base a must
be raised to equal a given number x.
y is equal to the logarithm, to the base a, of
x
This can be written using the implication sign ?
y loga x ? ay x
For example, 25 32 can be written in
logarithmic form as
log2 32 5
5
Logarithms
Taking a log and raising to a power are inverse
operations.
For example
2
6
6
Examples

• Rewrite as a logarithm 54 625
• 54 625
• 4 log5 625
• Find the value of log3 81
• log3 81 x
• 3x 81
• x 4 (because 34 81)

7
Task 1

• Exercise 3B 3C