IB DP Maths: AI SL复习笔记1.1.2 Exponents & Logarithms
Laws of Indices
What are the laws of indices?
- Laws of indices (or index laws) allow you to simplify and manipulate expressions involving exponents
- An exponent is a power that a number (called the base) is raised to
- Laws of indices can be used when the numbers are written with the same base
- The index laws you need to know are:
These laws are not in the formula booklet so you must remember them
How are laws of indices used?
- You will need to be able to carry out multiple calculations with the laws of indices
- Take your time and apply each law individually
- Work with numbers first and then with algebra
- Index laws only work with terms that have the same base, make sure you change the base of the term before using any of the index laws
- Changing the base means rewriting the number as an exponent with the base you need
Exam Tip
- Changing the base means rewriting the number as an exponent with the base you need
- Index laws are rarely a question on their own in the exam but are often needed to help you solve other problems, especially when working with logarithms or polynomials
- Look out for times when the laws of indices can be applied to help you solve a problem algebraically
Worked Example
Introduction to Logarithms
What are logarithms?
Why use logarithms?
- Logarithms allow us to solve equations where the exponent is the unknown value
- We can solve some of these by inspection
- For example, for the equation 2x= 8 we know that x must be 3
- Logarithms allow use to solve more complicated problems
- For example, the equation 2x = 10 does not have a clear answer
- We can solve some of these by inspection
Exam Tip
- Before going into the exam, make sure you are completely familiar with your GDC and know how to use its logarithm functions
Worked Example
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