Page 142 - Mathematics_Form_Two

Logarithms

3. The laws of logarithms are:
2. Determine the decimal numerals for
Logarithm of a product: each of the following:
(
5
log MN ) log M= a + log N (a) 9.15 × 10 (b) 8 × 10
–3
a
a
1
2
(d) 2.5 × 10
(c) 1.06 × 10
Logarithm of a quotient: a 3. Compute each of the following,
FOR ONLINE READING ONLY
M 

Mathematics for Secondary Schools Logarithm of a power: (a) (8 10 (12.5 10 − − 3 5 ) (8 10   − 15 ) )

log
log N
log M −
=

a 
give the answer in standard form:
a

N 
) ( 27.5 10
7
4
log (M) = plog M
P
(b)
a
a
Logarithm of identical power and
8 10
(c)

−
5 10
1
base: log a =
a
Logarithm of a root: (d) 1.728 10 5 2
n
log a m x = m log x 1.2 10 3 2 2 4
n
a
4. The conversion formula from log x (e) 2.5 10× ( ) (1.5 10× × ) ( 2.0 10− × )
log x = a . (1.2 10× 2 −× − 1 )
6 10
b
log b x
to log x is given by log x = log a a . (f) 5.0 10× 2

b
b
log b
a
5. The principles of calculating the 3 − 2
logarithms depend on the laws of (g) (1.2 10× ) ( 2.1 10× × )
exponents. 4 10× 2
That is; (h) 6.13 10× − 10 + 3.89 10× − 8
(i) when multiplying, add logarithms,
4. Find the value of x in each of the
(ii) when dividing,subtract, and following:
(iii) when raising to a power, multiply (a) log x =
4
8
by the exponent.  1 
(b) log x   125   = − 3
Revision exercise 6
3
(c) log x =
1. Write each of the following numbers
in standard form: 5. Determine the value of x in each of
the following:
(a) 8 419 000 (d) 0.000123
(
(a) log x2+3x−44)=1
(b) 45.7 (e) 4
(b) log(2x + 1) 0=
(c) 716 (f) 0.005 6. Determine the number whose
logarithm is defined as follows:
136
Student's Book Form Two
MATHEMATIC F2 v5.indd 136 11/10/2024 20:13:07
MATHEMATIC F2 v5.indd 136
11/10/2024 20:13:07