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- 1.5 Laws of exponents with integer exponents. Introduction to logarithms with base 10 and e.
- 1.7 Laws of exponents. Solving exponential equations, including using logarithms.

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Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.

- Indices A self marking exercise on indices (powers or exponents) including evaluating expressions and solving equations.
- Indices Pairs The traditional pairs or pelmanism game adapted to test knowledge of indices.
- Indices Video Indices, exponents and powers can all be used as a short way to describe repeated multiplication.
- Indices True False Arrange the given statements involving indices to show whether they are true or false.
- Dr Tim's Indices Challenge Dr Tim Honeywill has come up with these challenges to test your understanding of indices and algebra.
- Logarithms Self-marking exercises on evaluating logarithms and using them to solve equations.

Here are some exam-style questions on this topic:

- "
*(a) The \(n\)th term of a sequence is \(2^n+2^{n+1}\)*" ... more - "
*If a, b and c are positive integers use the following statements to find the values of a, b and c.*" ... more - "
*Find the value of the following:*" ... more - "
*Evaluate the following, giving your answers as integers.*" ... more - "
*Find the value of*" ... more - "
*In an old science fiction book the author described the intensity of reverse polarity, \(P\) measured in treckons, is a function of the nebula thrust, \(N\) measures in whovians. The intensity level is given by the following formula.*" ... more - "
*(a) Solve \(4x^2 - 8x - 5 = 0\)*" ... more - "
*(a) Show that \( \log_4 (\sin 2x +2) = \log_2 \sqrt{\sin 2x + 2 }\)*" ... more - "
*An arithmetic sequence has \(u_1 = \log_h(j)\) and \(u_2 = \log_h(jk)\), where \(h > 1\) and \(j, k \gt 0\).*" ... more - "
*Consider the function \(f (x) = \log_p(24x - 18x^2)\) , for \(0 \lt x \lt 1\), where \(p \gt 0\).*" ... more - "
*Two functions are defined as follows: \(f(x) = 2\ln x\) and \(g(x) = \ln \frac{x^2}{3}\).*" ... more

Here are some Advanced Starters on this statement:

**Log Perfection**

Determine whether the given statements containing logarithms are true or false more**Logarithm Equation**

Solve an equation containing logarithms with different bases more**Product of Indices**

Find the product of the unknown indices that feature in two equations more**Same Three Digits**

Find expressions which contain indices and evaluate to numbers containing the same digits. more **Seventeen Camels**

Explain the mathematics of the classic ninteenth century fraction sharing story. more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

- Indices Where do many fish live? Indices (in the seas!) This topic involves the use of the index, power or exponent. The concept is easily misunderstood and a surprisingly large number of pupils will evaluate 62 as 12 and not 36. After having mastered positive integer indices pupils should move on to negative indices and fractional indices. Exploring this topic in both numeric and algebraic ways will provide understanding and competence in this important concept.
- Logarithms Older teachers will remember their school days, before calculators were widely available, using logarithms to perform difficult multiplication and division calculations. Nowadays logarithms, or logs as they are more commonly known, are studied as part of an A Level and International Baccalaureate course and are seen as being useful for solving certain exponential equations. Basically a logarithm is the inverse function to exponentiation.

This Scheme of Learning was produced by White Rose Maths and is used here with permission granted on 30th June 2021.