Page 143 - Mathematics_Form_Two

Logarithms

(a) base 10 is 6 (a) Write the two equation
(b) base 6 is 6. connecting log x and log y .
a
a
7. Given thatlog x = 8.0524 , find the (b) Determine the value of log x
a
and log y .
value of log x . a
3
3
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8. Given that log 2 0.30103= , (c) Evaluate log a ( yx )
log5 0.69897= , and log7 0.84510= , 15. The intensity level L in decibels
 35   I 
find the value of log   2   without (dB) is given by L = 10 log   I 0   ,

using a calculator. where I is sound intensity and I is Mathematics for Secondary Schools
0
9. Without using calculator, determine the reference sound intensity. If the
the value of log5 log8 4log2.- + intensity level is increased from 50
dB to 80 dB, calculate the factor by
10. Without using a calculator, simplify which the intensity I has increased.
each of the following:
16. A certain radioactive substance has a
log 10 − 0.2t
N
(a)  log100 decay formula ( ) t = N e . If the
0
log10 initial amount N is 200 grams and
0
(b) log 176 log 11− 4 the amount remaining is 50 grams
4
11. Use a calculator to find the logarithm after t years, find t .
of each of the following numbers: 17. Given that log b= c and log d= f ,
(a) 0.8008 (b) 724 079  bd  a 2 a
(c) 0.0002 (d) 23.9 express log a   in terms of c and
. f  d 
12. Find the value of x if:
(a) log x = − 4.3217 18. The amount in a bank account grows
rt
(b) log x = 2.5543 according to the formula A= Pe . If
the amount in the account triples in 5
(c) log 10 ( x + 15x ) = 2. years, find the annual growth rate r
2
assuming continuous compounding.
13. If log 2 ( x y 3 ) 15= and 19. The population of species grows
2
4
log 2 ( x y 3 ) = 27, find each of the according to the formula ()P t = Pe
kt
.
0
following: If the population doubles in t years,
(a) log x (b) log y find the value of k in terms of .t
2
2
4
8
14. Given that log xy = and 20. Find the value of x for each of the
following equations.
a
 x  2 2
log a  3  = − 6: (a) log 10 ( x − ) 4 = 2log 10 ( x − ) 2 .
 y 
(b) 2 − 2 −=
2x
x
60
137
Student's Book Form Two
MATHEMATIC F2 v5.indd 137 11/10/2024 20:13:08
MATHEMATIC F2 v5.indd 137
11/10/2024 20:13:08