Worked solutions for example 5 Workshop 2 - Basic Algebra OES Contextual problems

1. 5 Rearrange the equation to make I the subject.
− log 훾푖 =
2 퐼
퐴푧푖
0퐵 퐼
1 + 훼푖

2. 0B I):
5 • Multiply both sides by (1 + αi

3. 0B I):
5 • Multiply both sides by (1 + αi
0B I) = Azi
− log γi (1 + αi
2 I

4. 0B I):
5 • Multiply both sides by (1 + αi
0B I) = Azi
− log γi (1 + αi
2 I
• Expand the brackets:

5. 0B I):
5 • Multiply both sides by (1 + αi
0B I) = Azi
− log γi (1 + αi
2 I
• Expand the brackets:
0B I log γi = Azi
− log γi − αi
2 I

6. 0B I):
5 • Multiply both sides by (1 + αi
0B I) = Azi
− log γi (1 + αi
2 I
• Expand the brackets:
0B I log γi = Azi
− log γi − αi
2 I
• Move everything containing I to one side:

7. 0B I):
5 • Multiply both sides by (1 + αi
0B I) = Azi
− log γi (1 + αi
2 I
• Expand the brackets:
0B I log γi = Azi
− log γi − αi
2 I
• Move everything containing I to one side:
2 I + αi
− log γi = Azi
0B I log(γi)

8. 0B I):
5 • Multiply both sides by (1 + αi
0B I) = Azi
− log γi (1 + αi
2 I
• Expand the brackets:
0B I log γi = Azi
− log γi − αi
2 I
• Move everything containing I to one side:
2 I + αi
− log γi = Azi
0B I log(γi)
• Collect like terms of I and factorise:

9. 0B I):
5 • Multiply both sides by (1 + αi
0B I) = Azi
− log γi (1 + αi
2 I
• Expand the brackets:
0B I log γi = Azi
− log γi − αi
2 I
• Move everything containing I to one side:
2 I + αi
− log γi = Azi
0B I log(γi)
• Collect like terms of I and factorise:
2 + αi
− log γi = I Azi
0B log(γi

10. 0B I):
5 • Multiply both sides by (1 + αi
0B I) = Azi
− log γi (1 + αi
2 I
• Expand the brackets:
0B I log γi = Azi
− log γi − αi
2 I
• Move everything containing I to one side:
2 I + αi
− log γi = Azi
0B I log(γi)
• Collect like terms of I and factorise:
2 + αi
− log γi = I Azi
0B log(γi
2 + αi
• Divide both sides by Azi
0B log(γi) :

11. 0B I):
5 • Multiply both sides by (1 + αi
0B I) = Azi
− log γi (1 + αi
2 I
• Expand the brackets:
0B I log γi = Azi
− log γi − αi
2 I
• Move everything containing I to one side:
2 I + αi
− log γi = Azi
0B I log(γi)
• Collect like terms of I and factorise:
2 + αi
− log γi = I Azi
0B log(γi
2 + αi
• Divide both sides by Azi
0B log(γi) :
− log γi
2 + αi
Azi
0B log(γi
= I

12. 0B I):
5 • Multiply both sides by (1 + αi
0B I) = Azi
− log γi (1 + αi
2 I
• Expand the brackets:
0B I log γi = Azi
− log γi − αi
2 I
• Move everything containing I to one side:
2 I + αi
− log γi = Azi
0B I log(γi)
• Collect like terms of I and factorise:
2 + αi
− log γi = I Azi
0B log(γi
2 + αi
• Divide both sides by Azi
0B log(γi) :
− log γi
2 + αi
Azi
0B log(γi
= I
• Square both sides:

13. 0B I):
5 • Multiply both sides by (1 + αi
0B I) = Azi
− log γi (1 + αi
2 I
• Expand the brackets:
0B I log γi = Azi
− log γi − αi
2 I
• Move everything containing I to one side:
2 I + αi
− log γi = Azi
0B I log(γi)
• Collect like terms of I and factorise:
2 + αi
− log γi = I Azi
0B log(γi
2 + αi
• Divide both sides by Azi
0B log(γi) :
− log γi
2 + αi
Azi
0B log(γi
= I
• Square both sides:
− 퐥퐨퐠 후퐢
ퟐ + 훂퐢
퐀퐳퐢
ퟎ퐁 퐥퐨퐠(후퐢
ퟐ
= 퐈