This document introduces logarithms and how to use them to solve exponential equations. It defines logarithms as the power to which a base number must be raised to equal the value being logged. Examples are provided of writing numbers and powers as logarithms in different bases. The basics are explained, such as the logarithm of the base number being 1 and logarithms of 0 or 1 not being possible. Students are directed to an online worksheet and book exercises to practice solving logarithmic equations.

1. Logarithms
By the end of the lesson you will be able to :
• Understand what a logarithm is.
• Find logarithms of numbers in different bases.
• Use logarithms to re­write exponential expressions.

2. Solve the equations:
3x
=3 (7x+6)2

3. 2x
= 5
Logarithms will help us to solve these type of
equations.
In the previous equation, , 8 can be
expressed as a power of 2.
But that is not the case with 5.

4. Definition:
( a > 0, a ≠1 )
log2 8 = 3 because 23
=8
log10 100 =

5. log2 32 =
log3 27 =
log10 0.1 =
log7 1=

6. log4 2 =
log5 0.2 =

7. log10 1 =

8. Write these powers as logarithms:
43
= 64
10­2
=0.01

9. Basics:
log2 2 = log7 7 =
loga a = 1

10. log7 1 = log4 1 =
loga 1 = 0
log 4 0 = loga 0 not possible
log10 is written log

11. Solve worksheet :
"Understanding logarithms"
http://www.maths­bingo.com/A%20enviar/LogarithmsDetermine/LogarithmsDetermine.html
Solve Book page 54­55 Ex 2D