Mathematics Assignment

Mathematics Assignment
Student Name:
Instructor Name:
Course Number:
12th May 2019

1a Using the laws of indices, for numbers having the same bases their powers
are added and subtracted if they are multiplied and divided respectively.
2 a2 b−4
6 c−4 × c 2
b2 a2
¿ a2 b− 4
3 a2 b2 × c 2
c−4
= b−6 c6
3
b) A number raised to a given power when again raised to another power, then
the final powers is the product of the initial powers.
¿ ) 4 ( a2 b2
b6 )
=2 a12 b−20×( a2 b2
b6 )
=2 a12 a2×( b2 b−20
b6 )
=2 a14 b−24
= 2 a14
b24
2a ¿ 9 ¿2( j+1 )=91
Equating the powers because the bases are equal we have.
2(j+1) =1
2j+2 =1
2j= -1
j= - 1
2

b) 53 ( j−3) ×54 j=52 (2 j+6)
Equating the powers we have
= 3(j-3) +4j=2(2j+6)
= 3j-9+4j=4j+12
=3j=21
j=7
3 a) ac=b
b) 70.463=x
2.462=x
c) 43 x−2=65
(3x-2) log 4=log 65
0.6021(3x-2) =1.81291
1.8063x-1.2042=1.8129
1.8063x=1.2042+1.8129
1.8063x=3.0171
x = 1.670
4 a) It is an exponential decay.
When x=0, y=100 and when x=3, y=6.4
The values of y decreases with increase in x values hence
exponential decay.