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 needExam Tip

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 2^x= 8 we know that?x?must be 3
  • Logarithms allow use to solve more complicated problems
    • For example, the equation 2^x?= 10 does not have a clear answer