LOGARITHMS

CONTENT

1. Deducing logarithm from indices and standard form
2. Definition of Logarithms
3. Definition of Antilogarithms
4. The graph of y = 10^x
5. Reading logarithm and Antilogarithm tables

Deducing Logarithm From Indices and Standard Form

There is a close link between indices and logarithms

100 = 10². This can be written in logarithmic notation as log₁₀100 = 2.

Similarly 8 = 2³ and it can be written as log₂8 = 3.

In general, N = b^x in logarithmic notation is Log_bN = 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 = 10³ (ii) 0.01 = 10⁻² (iii) 2⁴ = 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.