Page 139 - Mathematics_Form_Two
P. 139
Logarithms
3. Use a calculator to find the logarithm Activity 6�3: Exploring applications
of each the following numbers giving of logarithms in daily
the answer correct to 4 decimal life
places. 1. Using various exploration methods
(a) 8725 (g) 20 such as searching through the internet,
reading books and interviewing
FOR ONLINE READING ONLY
(b) 700.1 (h) 1986 experts, explore the applications of
(c) 76 408 (i) 78085.9 logarithms in daily life.
(d) 4 300 000 (j) 354 2. Using logarithm laws, demonstrate
(e) 83.7 (k) 43.657 how real life problems are solved. Mathematics for Secondary Schools
(f) 111 327 (l) 493 000 3. Share your findings with others
through demonstrations and other
4. Determine a number whose methods of your choice.
logarithm is: (give the answer correct
to 4 significant figure) Example 6�25
(a) 3.6156 (e) 0.07783
(b) 1.8937 (f) 3.8567− Solve the equation 7 x+ 1 = 90 . Give you
(c) 0.4515 (g) 1.2466 answer into 4 decimal places.
(d) 8 (h) 6.7515− Solution:
Given 7 x+ 1 = 90.
5. (a)If log x = 3.1425, determine x . Taking logarithm on both sides gives
(b) If log x = 2.5543, determine 4 . x log (7 x+ 1 ) log 90=
(c) If log x = 4.3217, find the value (x + 1)log7 = log 90
log
1
3
of x . x += log 90 , x = log90 − 1
log 7 log7
6. Find the value of x in each of the Using a calculator, x = 1.3124
following:
(a) log x = 2.9285 Example 6�25
(b) log x = 1.6990 The pH of a solution is given by the
formula pH = − log H + . If the
Applications of Logarithms hydrogen ion concentration, H + of
Logarithms are used in solving problems pure water is 1 10 M× − 7 , calculate the
involving exponential relationships. pH of pure water.
Logarithms are widely applied in real-
life situations such as measuring pH in Solution
chemistry, calculating compound interest Given pH = − log H + and
in finance, and determining earthquake H + = × − 7 .
1 10 MM
magnitudes.
133
Student's Book Form Two
11/10/2024 20:13:04
MATHEMATIC F2 v5.indd 133 11/10/2024 20:13:04
MATHEMATIC F2 v5.indd 133
