Page 141 - Mathematics_Form_Two

Logarithms

(c) log n = log 2 9. The intensity level L of sound is
5
4
(d) log 15 3= 90 dB. Calculate the sound intensity
m
1 10
(e) 5 x+ 2 − 5 = x 20 I if I =× − 12 watts/m², given
0
(f) 2 −× x 6 0= L = 10 log   I   .
52 +
2x
 I 0 
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2. The pH of a solution is 7. Calculate 10. The population of a certain bacteria

the hydrogen ion concentration H  +  grows according to the formula

using the formula H    +  = 10 − pH . P ()t = Pe . If the initial population
rt
0
2
3. Solve x given (log x) + 12 = log x 7 is 200 and the population doubles in Mathematics for Secondary Schools
2
2
4. A population grows exponentially 5 hours, calculate the growth rate .r
according to the formula ()P t = Pe 11. Solve the following simultaneous
rt
,
0
where P is the initial population, r equations
0
is the growth rate, and t is time. If  2 = 82× y
x
the initial population is 500 and the (a) 
growth rate is 2%, how long will it  log(2x − 3 ) 1y =
take for the population to reach 1000? (b)
5. Using the compound interest formula  log (y + 3) 1 log x−= 2
2

+
=
t
A= P (1 r+ ) , calculate the time t  log (x + 2 4) log (x − 2 4) log (y − 2 2)
needed for an investment to double if
the interest rate r= 4% annually.
 I  Chapter summary
6. Rearrange the formula L= 10 log  
 I 0  1. A number in standard form is written
to solve for I , then calculate I if as A × 10n, where 1 ≤ A < 10 and n

1 10
L= 80 dB and I =× − 12 watts/m². is an integer.
0
7. The decay of a substance over time 2. A number in exponential form can
be expressed in logarithmic form as
is given by N ()t = Ne − t λ where N shown in the following table.
0
0
is the initial quantity,  is the decay Exponential Logarithmic
constant, and t is time. If N= 500
0
and Nt = 250 after 10 years, form form
( )
calculate the value of .λ 1000 10= 3 log 1 000 = 3
10
8. Using the compound interest formula 1 10= 0 log 1 0=
10
t
A= P (1 r+ ) , calculate the time t –2
needed for an investment to triple its 0.01 = 10 log 0.01 = –2
10
initial value if the interest rate is 5% Generally, if x = a , then log x = .
b
b
annually. a
135
Student's Book Form Two

11/10/2024 20:13:06
MATHEMATIC F2 v5.indd 135
MATHEMATIC F2 v5.indd 135 11/10/2024 20:13:06