Logarithms

Logarithms are a way of plotting numbers in scientific notation. The logarithm of a number, written log(number), is the power of ten that it equals. Here are some examples:

log (10²) = 2

log (10⁴³) = 43

log (10^-4) = -4.

Logarithms can also express numbers that are not even powers of ten. For example, 3.16 = 10^0.5, so

log (3.16) = 0.5.

The logarithm of a number times another number is the sum of the logarithms of the numbers, so

log (3.16 x 10³ ) = 0.5 + 3 = 3.5.

Although this is potentially a large subject, these short notes should help you understand graphs in terms of logarithms, which we will use from time to time in this course because they are the only way to plot scientific notation without losing its ability to express a large range of values.