12.2 - Logarithms<span>Before reading this section you may want to review the section on </span>exponents<span>, since logarithms are based on them. </span>
<span>Introduction: </span><span>It is a fact that every positive number, </span>y<span>, can be written as 10 raised to some power, </span>x. We write this relationship in equation form, like this:<span>y = 10 x.</span>For example it is quite obvious that 1000 can be written as 10 3, because the exponent 3 means multiply 10 by itself 3 times and 10·10·10=1000. It may not be quite so obvious that 16 can be written as 10 1.2. What does it mean to multiply something by itself 1.2 times? And how can we calculate that this is the correct power of 10? The answer is in the graph shown below.
This is a graph of the equation y = 10 x that was mentioned above. To make this graph we made a table of a few obvious values of y = 10 x<span> as shown below, left. Then we plotted the values in the graph (they are the red dots) and drew a smooth curve through them. Then we observed that the curve went through </span>y<span> = 16 and </span>x<span> = 1.2 (the black dot). We take this to mean that 16 = 10</span> 1.2<span>. </span>
To find the number of neutrons, you subtract the atomic number from the mass number of element X. So in this case, it'll be 151-44= the number of neutrons.
