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# Theory Of Logarithms And Laws Of Logarithms

In general the logarithm of a number is the power to which the base must be raised in order to give that number. i.e if y=nx, then x = logny. Thus, logarithms of a number to base ten is the power to which 10 is raised in order to give that number i.e if y =10x, then x =log10y. With this definition log10100= 3 since 103= 1000 and log10100 = 2 since 102=100.

#### Further Application of Logarithms using tables:

Examples:

Use the tables to find the log of:

(a) 37     (b) 3900 to base ten Solutions

1. 37 = 3.7 x 10

=3.7 x 101(standard form)

=100.5682 + 1 x 101 (from table)

=101.5682

Hence log1037 = 1.5682 2. 3900 = 3.9 x 1000

=3.9 X 103  (standard form)

=100.5911 x 103  (from table)

=100.5911 + 3

=103.5911

Therefore log103900 = 3.5911

## Solving Logarithmic Equations

Reading assignment: NGM for SSS BK1 pg 18 – 22 and ex. 1c Nos 19 – 20 page 22

#### Weekend Assignment

1. Find the log of 802 to base 10 (use log tables) (a) 2.9042 (b) 3.9040 (c) 8.020 (d)1.9042

2. Find the number whose logarithm is 2.8321 (a) 6719.2 (b) 679.4 (c) 0.4620 (d) 67.92

3. What is the integer of the log of 0.000352 (a) 4 (b) 3 (c) 4 (d)3 4. Given that log2(1/64) = m, what is m ? (a) -5 (b) -4 (c) -6 (d) 3

5. Express the log in index form: log1010000 =4 (a) 103 = 10000 (b) 10-4 = 10000 (c) 104 = 10000

(d) 105 =100000

#### Theory

1. Evaluate using logarithm table 6.28 x 304