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Indices, logs, surds


Indices are also known as powers or exponents. Exponential growth or decay can describe changes in population or the spread of a disease. Logarithms and indices are vital for all areas of STEM, finance, geography and epidemiology.

See also Percentages & surds

  • ILS1.1 Indices

    What is index notation? When a number such as 16 is written in the form 42 (which means 4 x 4) we say that it is written as an exponential, or in index notation. There are laws about multiplying and dividing indices as well as how to deal with negative indices.

  • ILS1.2 Fractional indices

    Can an index also be a fractional number? An index can be an integer – a counting number - either positive or negative. An index can also be a fraction such as ½, ¾, or 2.5.
    Read this section to see what this means, and how the laws of indices apply to fractional indices.

  • ILS2.1 Logarithms

    What is a logarithm? The logarithm of a number is the power that the base must be raised to, to give that number. The logarithm of 16 with a base of 2 is 4, because 24 = 16.

  • ILS2.2 Exponential equations

    We know that 32 is 9 and 33 is 27. But what is the power of 3 that is equal to something in between, such as 20? It would be 3 to the power of something greater than 2 but less than 3. Logarithms and exponential equations can help us here.
    Read this section to see how to solve exponential equations.

  • ILS3.1 Simplifying surds

    What happens if you want to take the root of larger surds? These may be factorised down to numbers that may or may not be surds.
    Read this sheet to see how larger surds can be factorised out and expressed as a combination of both rational numbers and surds.