Page 128 - Mathematics_Form_Two

Logarithms

Special cases of logarithms Exercise 6�2
The following are some special cases on 1. Write each of the following
logarithms of numbers: expressions in logarithmic form:
(a) 2 = 16 (b) 5 = 25
4
2
x
1
x
1. If log a = , then a = a which
a
3
5
1
gives x = . a 1. (c) 3 = 243 (d) 4 = 64
FOR ONLINE READING ONLY
1
Mathematics for Secondary Schools Thus, log 10 1= and log 2 1= . n (g) 10 = 1 0.001 (h) 13 = 10 1 − 1 1
Therefore, log a =
(f) 3 =
6
(e) 10 = 1,000,000
−
2
9
0
13
1
10
2
(j) 10 =
(i) 10 =
−
3
( )
n
x for a positive number
2. If log a =
a
2
16
4
a; then a =

n
a , which gives x = .
x
1
−
23 =
(l)
(k)
=

3
9

=
n
. n
Therefore, log ( )a
a
3. If a = 1, then log 1 = 0. Thus, 2. Write each of the following 23
0
a
logarithm of 1 to any base is 0. expressions in exponential forms:
Base 10 logarithms (a) log 121 2=
11
10,000 = 4
Base 10 logarithms are logarithms of (b) log 10 000
10
numbers to base 10, also known as (c) log 0.1= − 1
10
common logarithms. The base 10 is 1
usually left out when writing common (d) log 2 = 2
4
logarithms to base 10. For instance, (e) log 0.25 = − 2
2
instead of writing log 315 it is simply æ 1 ö
10
written as log315. In general, log x is (f) log 1 ç 5 è 125 ø ÷ = 3 - 3
10
written as log x.
3. Find the value of x in each of the
The following are some logarithms of following equations:
numbers which are powers of integral (a) log x = 2
exponents of 10: 2
2
log100 = log10 = 2 (b) log 1 x=
5
1
log10 = log10 = 1 (c) log x = 1
5
log1 log10= 0 = 0 (d) log x = − 3
4
log0.1 log10= - 1 = - 1 (e) log 256 x=
4
log0.01 log10= - 2 = - 2 (f) log 10 1=
log0.001 log10= - 3 = - 3 x
n
In general, log10 = n (g) log 2 ç æ 1 ö ÷ = x
è 1 024 ø
122
Student's Book Form Two
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MATHEMATIC F2 v5.indd 122 11/10/2024 20:12:52
MATHEMATIC F2 v5.indd 122