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
- Evaluate using logarithm table 6.28 x 304
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