Logarithms Revision Notes for Core 2

Notes I created for logarithms. It is not to bad when you get your head around the laws of log etc, and should soon become easy marks in a C2 paper :)

HideShow resource information
  • Created by: George
  • Created on: 12-05-11 18:20
Preview of Logarithms Revision Notes for Core 2

First 191 words of the document:

Mathematics ­ Core 2 Logarithms
How to write an expression as a logarithm
Log a n = x could be written in the form a x = n, where a is called the base of the logarithm.
This is key for answering many log questions!
Laws of logarithms
If log a x = b and log a y = c
a b= x and a c = y (using the law from above)
Multiplication Law
xy = a b x a c = a b + c
log a xy = b + c (using the rule from above `how to write an expression as a logarithm)
log a xy = log a x + log a y
Division law
x / y = a b / a c = a b c
log a (x / y) = b ­ c
log a (x / y) = log a x ­ log a y
Power law
If we let x = log a y
Writing in other form: a x = y
Raise each side to the power z: (a x) z = y p
Writing back into logarithm form: log a y p = x z

Other pages in this set

Page 2

Preview of page 2

Here's a taster:

Substitute x = log a y back in: log a y z = z (log a y)
Examples
Rewrite 5 4 = 625 as a logarithm
a x = n => Log a n = x
5 4 = 625 => log 5 625 = 4
Write a single logarithm:
Log 3 6 + log 3 7 (multiplication law)
Log 3 42
2log 5 3 + 3log 5 2 (power law and multiplication law)
log 5 3 2 + log 5 2 3
log 5…read more

Page 3

Preview of page 3

Here's a taster:

­ log 7) / (log 7 ­ log 3)
x = 0.2966
Changing the base of the logarithms
Suppose that log a x = m
A m = x
Take logs to the base b: log b a m = log b x
m log b a = log b x
Substitute back in m
log a x .…read more

Page 4

Preview of page 4

Here's a taster:

Exam Questions
Find the values of x such that:
(log 2 32 + log 2 16) / log 2 x = log 2 x
The easiest way to solve this logarithm question would be through the use of substitution
because we have two terms that are identical.…read more

Page 5

Preview of page 5

Here's a taster:

­ 21) = 0
x = 0 and x = 21 (x can't be a solution because it's not > 0)
x = 21…read more

Comments

TayaMairead

Really helpful to summarise laws of logs :)

aroojyousaf

thank you for this! very helpful

Similar Mathematics resources:

See all Mathematics resources »See all resources »