Page 140 - Mathematics_Form_Two
P. 140
Logarithms
Substitute the value of the hydrogen Example 6�27
ions into the formula to get The Richter scale measures the
pH − log 1 10 × = − 7 magnitude M of an earthquake based
on the energy released by using the
Using the laws of logarithms or calculator E
to determine the logarithm gives formula M = log E 0 0 , where E is the
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Mathematics for Secondary Schools Example 6�26 energy. If an earthquake recorded a
7
pH =
energy released and E is the standard
Therefore, the pH of pure water is 7.
magnitude of 8 with standard energy
E =
10 Joules, what was the energy
4
0
released?
The formula for determining a compound
) , where
interest is given by A =
P
(1 r+
t
A is the final amount, P is the principal, Solution E
4
r is the annual interest rate, and t is the Given M = log E 0 , E = 10 Joules,
0
time in years. Find the number of years M = 8.
it will take for the principal to double Substituting these values into the
if r = 5%. formula gives
Solution 8 log= E 4
Given A = 2,P r = 5% , A = P (1 r+ ) t 10
t
From A = P (1 r+ ) , substitute the given Applying writing into exponential form
values to get gives,
E 8
2P = P (1 0.05)+ t 10 4 = 10
2 (1.05)= t E = 10 × 10 4
8
Apply logarithms on both sides and = 10 12
simplify to obtain, Therefore, the energy released by the
12
earthquake is 10 Joules.
log 2 log(1.05)= t
log 2 t= log(1.05) Exercise 6�5
log 2
t = Whenever required, take e= 2.7183.
log(1.05) 1. Solve each of the following
Using a calculator to find the value of t exponential equations giving the
gives t = 14.2. answers correct to 4 decimal places.
Therefore, the principal will double after (a) 3 = 2 x− 1
x
14.2 years. (b) 4 1.5× x = 30
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Student's Book Form Two
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MATHEMATIC F2 v5.indd 134 11/10/2024 20:13:05
MATHEMATIC F2 v5.indd 134
