Maths for Diploma Studies

Logarithms are a bit like a mirror image of exponents. Taking the logarithm of a number, we find the exponent to which a base number is raised to produce that number.

Our exponent in this exponentiation equation:

10² = 100

becomes our logarithm in this equation:

So the logarithm to the base 10 of 100 is 2 because 10 to the power of 2 is 100.

We call the number that has been raised by the power of the exponent the base and, in this case, the most common base, base 10. Funnily enough, it is also sometimes called the common log.

The word logarithm was made up by Scottish mathematician John Napier. He combined the Greek words logos meaning ratio and arithmos meaning number to make a word meaning ratio-number.

Another way to look at logarithms is that they are the number of times we need to multiply the base together to get the product. In the case above, the number of times we need to multiply 10 together to get 100.

To test our understanding. What is the base and logarithm in this equation?

Give yourself 5-10 minutes to think about this, and then click ‘Next’ to continue with this lesson