SS1 First Term Mathematics Lesson Note – Logarithms

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WEEK 2           

TOPIC: 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 = 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) = 16 (iv)  = 2^-3

Change the following to index form

• Log₄16 = 2 (ii) log₃ ( ) = -3

The logarithm of a number has two parts and integer (whole number) then the decimal point. The integral part is called the characteristics and the decimal part is called mantissa.

To find the logarithms of 27.5 form the table, express the number in the standard form as 27.5 = 2.75 x 10¹. The power of ten in this standard form is the characteristics of Log 27.5. The decimal part is called mantissa.

Remember a number is in the standard form if written as A x 10ⁿ where A is a number such that 1 ≤ A < 10 and n is an integer.

27.5 = 2.75 x 10^1,  27.5 when written in the standard form, the power of ten is 1. Hence the characteristic of Log 27.5 is 1. The mantissa can be read from 4-figure table. This 4-figure table is at the back of your New General Mathematics textbook.

To check for Log27.5, look for the first two digits i.e 27 in the first column.

Now look across that row of 27 and stop at the column with 5 at the top. This gives the figure 4393.

Hence Log27.5 = 1.4393

To find Log275.2,     2.752 x 10²

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