Edexcel AS Level

Law of logarithms – Paper 1

4 Topics | 3 Quizzes

What is a Logarithm?

Anticlockwise Trick for logs

Logarithms Bronze

Rules for Logarithms you need to know

Logarithms Silver

Logarithms Gold

Logarithms : Solving disguised quadratics in exponential Functions (Additional)

Paper 1

3 Topics

Proof by Exhaustion and Deduction

Example to Try on Proof by Exhaustion and Deduction

Proof by using a Counter-Example

4 Topics | 4 Quizzes

How to factorise a cubic equation (Method 1)

The Factor Theorem

Algebraic Division Bronze

Algebraic Division Silver

Algebraic Division Gold

How to solve a cubic equation using the factor theorem

How to factorise a cubic polynomial (Method 2)

Polynomials Gold

Graphs of functions

6 Topics | 7 Quizzes

Sketching Quadratic Graphs

Quadratic graphs Bronze

Quadratic graphs Silver

Quadratic graphs Gold

Sketching Quadratic Graphs by Completing the Square (part 1)

Sketching Quadratic Graphs by Completing the Square (part 2)

GCSE Completing the Square Bronze

GCSE Completing the Square Silver

How to Sketch Cubic Graphs

Cubic graphs Bronze

Sketching Reciprocal graphs of the form y=k/x

Sketching graphs of the form k/x^2

Reciprocal graphs Silver

Roots of equations

8 Topics | 3 Quizzes

Simultaneous Equations – Elimination method – Tutorial 1

Simultaneous Equations – Elimination method – Tutorial 2

Simultaneous Equations – Elimination method – Tutorial 3

Simultaneous Equations – Elimination method – Tutorial 4

Simultaneous Equations – Elimination method – Tutorial 5

Simultaneous Equations – Elimination method – Tutorial 6

Simultaneous Equations – Substitution Method – Tutorial 1

Simultaneous Equations – Substitution Method – Tutorial 2

Simultaneous Equations Bronze

Simultaneous Equations Silver

Simultaneous Equations Gold

1 Topic

Factorising Quadratic Expressions

Coordinate Geometry, Straight Line

5 Topics | 3 Quizzes

How to find the Equation of a straight line y=mx+c

Coordinate Geometry : Equation of a parallel line

Coordinate Geometry : Equation of a perpendicular bisector

Coordinate Geometry – Distance between two points

Coordinate Geometry – Mid-point of a line segment

Equations of Straight Lines Bronze

Equations of Straight Lines Silver

Equations of Straight Lines Gold

Coordinate geometry of circles

6 Topics | 3 Quizzes

Circle Properties You Should Know

Equation of a circle

Equation of a Circle (Alternative form)

Equations of Circles Bronze

Finding the Centre and Radius of Circle

Equations of Circles Silver

Equation of a Circle passing through 3 points

Equation of a Tangent to a Circle

Equations of Circles Gold

1 of 4

Logarithms Bronze

Edexcel AS Level Law of logarithms – Paper 1 Anticlockwise Trick for logs Logarithms Bronze

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Question 1 of 25

1. Question
\(\text{Write as a logarithm: }\)\(32={2}^{5}\)
- \(5={\mathrm{log}}_{2}32\)
- \(5{\mathrm{log}}32\)
- \(2={\mathrm{log}}_{5}32\)
- \(5={\mathrm{log}}_{32}2\)
Correct

Incorrect
Question 2 of 25

2. Question
\(\text{Write as a logarithm: }\)\(1024={2}^{10}\)
- \(10={\mathrm{log}}_{2}1024\)
- \(10={\mathrm{log}}_{1024}2\)
- \(2{\mathrm{log}}_{10}1024\)
- \(1024={\mathrm{log}}_{10}2\)
Correct

Incorrect
Question 3 of 25

3. Question
\(\text{Write as a logarithm: }\)\(243={3}^{5}\)
- \(5={\mathrm{log}}_{3}243\)
- \(3{\mathrm{log}}_{5}243\)
- \(243{\mathrm{log}}_{3}5\)
- \(5={\mathrm{log}}_{243}3\)
Correct

Incorrect
Question 4 of 25

4. Question
\(\text{Write as a logarithm: }\)\(64={4}^{3}\)
- \(3={\mathrm{log}}_{4}64\)
- \(64={\mathrm{log}}_{4}3\)
- \(4{\mathrm{log}}_{3}64\)
- \(4={\mathrm{log}}_{64}3\)
Correct

Incorrect
Question 5 of 25

5. Question
\(\text{Write as a logarithm: }\)\(\frac{1}{32}={2}^{-5}\)
- \(-5={\mathrm{log}}_{2}\frac{1}{32}\)
- \(-5{\mathrm{log}}_{\frac{1}{32}}2\)
- \(-5{\mathrm{log}}_{2}\frac{1}{32}\)
- \(\frac{1}{32}{\mathrm{log}}_{2}-5\)
Correct

Incorrect
Question 6 of 25

6. Question
\(\text{Write as a logarithm: }\)\(\frac{1}{9}={3}^{-2}\)
- \(-2={\mathrm{log}}_{3}\frac{1}{9}\)
- \(\frac{1}{9}={\mathrm{log}}_{3}-2\)
- \(\frac{1}{9}{\mathrm{log}}_{3}-2\)
- \(3={\mathrm{log}}_{-}2\frac{1}{9}\)
Correct

Incorrect
Question 7 of 25

7. Question
\(\text{Write as a logarithm: }\)\(\frac{1}{25}={5}^{-2}\)
- \(-2={\mathrm{log}}_{5}\frac{1}{25}\)
- \(-2={\mathrm{log}}_{\frac{1}{25}}5\)
- \(\frac{1}{25}{\mathrm{log}}_{5}-2\)
- \(-2{\mathrm{log}}_{\frac{1}{25}}5\)
Correct

Incorrect
Question 8 of 25

8. Question
\(\text{Write as a logarithm: }\)\(\frac{1}{125}={5}^{-3}\)
- \(-3={\mathrm{log}}_{5}\frac{1}{125}\)
- \(\frac{1}{125}={\mathrm{log}}_{5}-3\)
- \(-3{\mathrm{log}}_{\frac{1}{125}}5\)
- \(\frac{1}{125}{\mathrm{log}}_{5}-3\)
Correct

Incorrect
Question 9 of 25

9. Question
\(\text{Write as a logarithm: }\)\(4={8}^{\frac{2}{3}}\)
- \(\frac{2}{3}={\mathrm{log}}_{8}4\)
- \(8={\mathrm{log}}_{\frac{2}{3}}4\)
- \(\frac{2}{3}={\mathrm{log}}_{4}8\)
- \(4={\mathrm{log}}_{\frac{2}{3}}8\)
Correct

Incorrect
Question 10 of 25

10. Question
\(\text{Write as a logarithm: }\)\(3={9}^{\frac{1}{2}}\)
- \(\frac{1}{2}={\mathrm{log}}_{9}3\)
- \(3={\mathrm{log}}_{9}\frac{1}{2}\)
- \(9={\mathrm{log}}_{\frac{1}{2}}3\)
- \(9={\mathrm{log}}_{3}\frac{1}{2}\)
Correct

Incorrect
Question 11 of 25

11. Question
\(\text{Write as a logarithm: }\)\(4={8}^{-\frac{2}{3}}\)
- \(-\frac{2}{3}={\mathrm{log}}_{8}4\)
- \(-\frac{2}{3}={\mathrm{log}}_{4}8\)
- \(4={\mathrm{log}}_{\frac{-2}{3}}8\)
- \(8={\mathrm{log}}_{\frac{-2}{3}}4\)
Correct

Incorrect
Question 12 of 25

12. Question
\(\text{Write as a logarithm: }\)\(2={4}^{-\frac{1}{2}}\)
- \(-\frac{1}{2}={\mathrm{log}}_{4}2\)
- \(4={\mathrm{log}}_{2}-\frac{1}{2}\)
- \(2={\mathrm{log}}_{\frac{-1}{2}}4\)
- \(2={\mathrm{log}}_{4}-\frac{1}{2}\)
Correct

Incorrect
Question 13 of 25

13. Question
\(\text{Write in index notation: }\)\(4={\mathrm{log}}_{2}16\)
- \(16={2}^{4}\)
- \(16={4}^{2}\)
- \({4}^{8}\)
- \({16}^{4}\)
Correct

Incorrect
Question 14 of 25

14. Question
\(\text{Write in index notation: }\)\(5={\mathrm{log}}_{2}32\)
- \(32={2}^{5}\)
- \(2={32}^{5}\)
- \(32={5}^{2}\)
- \({10}^{32}\)
Correct

Incorrect
Question 15 of 25

15. Question
\(\text{Write in index notation: }\)\(4={\mathrm{log}}_{4}256\)
- \(256={4}^{4}\)
- \(4={4}^{256}\)
- \({1024}^{4}\)
- \({16}^{256}\)
Correct

Incorrect
Question 16 of 25

16. Question
\(\text{Write in index notation: }\)\(5={\mathrm{log}}_{4}1024\)
- \(1024={4}^{5}\)
- \({5120}^{4}\)
- \({20}^{1024}\)
- \(4={1024}^{5}\)
Correct

Incorrect
Question 17 of 25

17. Question
\(\text{Write in index notation: }\)\(-2={\mathrm{log}}_{3}\frac{1}{9}\)
- \(\frac{1}{9}={3}^{-2}\)
- \(3={\frac{1}{9}}^{-2}\)
- \(\frac{1}{9}=-{2}^{3}\)
- \(-{6}^{\frac{1}{9}}\)
Correct

Incorrect
Question 18 of 25

18. Question
\(\text{Write in index notation: }\)\(-5={\mathrm{log}}_{4}\frac{1}{1024}\)
- \(\frac{1}{1024}={4}^{-5}\)
- \(-5={4}^{\frac{1}{1024}}\)
- \(\frac{1}{1024}=-{5}^{4}\)
- \(4={\frac{1}{1024}}^{-5}\)
Correct

Incorrect
Question 19 of 25

19. Question
\(\text{Write in index notation: }\)\(-3={\mathrm{log}}_{3}\frac{1}{27}\)
- \(\frac{1}{27}={3}^{-3}\)
- \(-{9}^{\frac{1}{27}}\)
- \(-3={3}^{\frac{1}{27}}\)
- \(\frac{1}{27}=-{3}^{3}\)
Correct

Incorrect
Question 20 of 25

20. Question
\(\text{Write in index notation: }\)\(-2={\mathrm{log}}_{3}\frac{1}{9}\)
- \(\frac{1}{9}={3}^{-2}\)
- \(-2={3}^{\frac{1}{9}}\)
- \(\frac{1}{9}=-{2}^{3}\)
- \(3={\frac{1}{9}}^{-2}\)
Correct

Incorrect
Question 21 of 25

21. Question
\(\text{Write in index notation: }\)\(\frac{1}{3}={\mathrm{log}}_{8}2\)
- \(2={8}^{\frac{1}{3}}\)
- \(2={\frac{1}{3}}^{8}\)
- \(8={2}^{\frac{1}{3}}\)
- \(\frac{1}{3}={8}^{2}\)
Correct

Incorrect
Question 22 of 25

22. Question
\(\text{Write in index notation: }\)\(\frac{2}{3}={\mathrm{log}}_{8}4\)
- \(4={8}^{\frac{2}{3}}\)
- \(8={\frac{2}{3}}^{4}\)
- \(\frac{2}{3}={8}^{4}\)
- \(\frac{2}{3}={4}^{8}\)
Correct

Incorrect
Question 23 of 25

23. Question
\(\text{Write in index notation: }\)\(-\frac{1}{2}={\mathrm{log}}_{4}2\)
- \(2={4}^{-\frac{1}{2}}\)
- \(4={2}^{-\frac{1}{2}}\)
- \(2=-{\frac{1}{2}}^{4}\)
- \(-\frac{1}{2}={2}^{4}\)
Correct

Incorrect
Question 24 of 25

24. Question
\(\text{Write in index notation: }\)\(-\frac{1}{3}={\mathrm{log}}_{8}2\)
- \(2={8}^{-\frac{1}{3}}\)
- \(-\frac{1}{3}={8}^{2}\)
- \(-\frac{1}{3}={2}^{8}\)
- \(8={2}^{-\frac{1}{3}}\)
Correct

Incorrect
Question 25 of 25

25. Question
\(\text{Write in index notation: }\)\(-\frac{1}{2}={\mathrm{log}}_{9}3\)
- \(3={9}^{-\frac{1}{2}}\)
- \(-\frac{1}{2}={3}^{9}\)
- \(9={3}^{-\frac{1}{2}}\)
- \(-\frac{1}{2}={9}^{3}\)
Correct

Incorrect

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