If you work through this section you should be able to:
A power or exponent of a number states how many times to multiply the number by itself. The power is called the logarithm of a number to the base.
For example, 25 = 32, then 5 = log2 32, which is spoken as 5 is the logarithm of 32 to the base 2.
Exponential form |
Logarithmic form |
---|---|
34 = 81 |
4 = log3 81 |
63 = 216 |
3 = log6 216 |
105 = 100000 |
5 = log10 100000 |
Because logarithms are powers, the rules of logarithms closely follow the rules of indices. The rules of logarithms are given as below:
1.
2.
3.
4.
=
=
=
5.
=
= 1.5
When a logarithm is written without a base, it usually means that the base is 10. It is called common logarithm. For example, log100 = log10100 = 2.
Another base that is often used is e (Euler's Number) which is about 2.71828. Logarithms to base e are called natural logarithms, which are denoted by loge or ln. For example, ln(7.389) = loge(7.389) ≈ 2.
Negative logarithms state how many to divide by the number.
For example, 2-4 =
We will now look at how to use logarithms to solve logarithmic equations.
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Solution
You can download a version of this Logarithms activity in Word format:
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