This table to the left clearly shows that the log of 2 numbers subtracted from each other will equal the log of the numbers divided by each other.The table below clearly shows the log () – log () will equal log (). Let log x = a, let log y = b. Therefore 10a = x and 10b = y, these two equations can be converted into 10(a – b) = x/y. Finally, this equation can then be converted back into log x – log y = log (x/y).

The table located to the left clearly shows that the log of a number multiplied by another number will equal the log of a number to the power of the multiplying number.This table below proves that will equal. 4 log 2 is producing log2 + log2 + log2 + log2, log 24 is producing log16. Log 16 counteracts the additional logs that need to be added together in 4 log2, it is doing this by decreasing the amount of logs that need to be added in log 16, and replaceing them with a higher x value.

Let’s investigate the function y = log x

When x = 1, y = log1, therefore, y = 0

Therefore when y = 0, x will equal 1. On a graph this would mean that the curve would cut the x axis at 1. In this function x cannot equal zero or less than zero, this means that the restricted domain of the function will be {x: x>1}.

The table above displays that as x is multiplied by ten, the y value increases by 1.

The graph below demonstrates the curve of the function y = log x