Topic Content:
- Relationship between Indices & Logarithms
Recall the laws of indices ;
1. \( \scriptsize a^x \: \times \: a^y = a^{x \:+\:y} \)
2. \( \scriptsize a^x \: \div \: a^y = a^{x \:-\:y} \)
3. \( \scriptsize a^0 = 1\)
4. \( \scriptsize \left (a^x \right)^y = a^{xy} \)
5. \(\scriptsize a^{-x} = \normalsize \frac {1}{a^x}\)
6. \( \scriptsize a ^{\frac{x}{y}} = \left ( \scriptsize \sqrt [y] {a} \right) ^x \)
7. \( \scriptsize a ^{\frac{1}{x}} = \sqrt [x] {a} \)
These laws are true for all values of x, y and a ≠0. It is common knowledge that scientific calculators have taken the place of logarithm and anti-logarithm tables. However, it is important to note that the theory of Logarithms is very relevant in science and technology.
Note that in index notation 34 = 81
Where 81 is the number , 3 is the base and 4 is the index or power.
But it can also be said that the logarithm of 81 to base 3 is 4.
i.e. 81 = 34 ……..(1)
and log3 81 = 4 ………(2)
It is important to note that equations (1) and (2) are equivalent.
34 = 81 is the index form while log3 81 = 4 is the logarithmic form.
It is necessary to understand how to change from one form to the other. The general form is given as:
If N = ax , then loga N = x
So we
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