Logarithms Revision Notes for Core 2

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…

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:…

x = (2log 3 ­ 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…

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.

Let log 2…

x (x ­ 21) = 0

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

x = 21