**LOGARITHMS**

CONTENT

- Deducing logarithm from indices and standard form
- Definition of Logarithms
- Definition of Antilogarithms
- The graph of y = 10
^{x} - Reading logarithm and Antilogarithm tables

**Deducing Logarithm From Indices and Standard Form**

There is a close link between indices and logarithms

100 = 10^{2}. This can be written in logarithmic notation as log_{10}100 = 2.

Similarly 8 = 2^{3} and it can be written as log_{2}8 = 3.

In general, N = *b ^{x}* in logarithmic notation is Log

_{b}N = x.

We say the logarithms of N in base *b* is *x*. When the base is ten, the logarithms is known as common logarithms.

The logarithms of a number N in base b is the power to which b must be raised to get N.

Re-write using logarithmic notation (i) 1000 = 10^{3} (ii) 0.01 = 10^{−2} (iii) 2^{4} = 16 (iv) 1/8 = 2^{−3}

Change the following to index form

(i) \(Log_416 = 2\)

(ii) \(Log_3 (\frac{1}{27}) = -3\)

The logarithm of a number has two parts and integer (whole number) then the decimal point.

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