There's a log function at the top where we can specify the base, let's instead use the log 10 function, which specifies 10 as the base. We see a list of potential functions pop up. Let's start by typing log into the formula bar. Now let's take the log of each of these results and it should return the same values we see in the exponent in column B. We see the formula returns the same result as the column next to it and in a more efficient way. We'll create a new formula and we'll use the exp function and we'll raise it to the value in column B. For the formulas that use Euler's number as the base, we can set up this calculation directly using the Excel exp function which raises Euler's number to the parameter value we pass to it. We see the result is 100 and we can copy the rest of the formulas down.
In the results one column, we'll set the equation equal to the base in column A, raised to the exponent in column B.
We have some values in the first column for base 10 and Euler's number, in the column next to that, we have the exponent we want to raise the number to, and to the right of that, we have some other columns we're going to fill in with our exponent and logarithm calculations. So be careful because this often depends on the context of what you're talking about or the programming language we're utilizing. Often log and natural log are used interchangeably. The exponent we raised the Euler's number to get a result is the result we get when we take the natural logarithm at this result. Logarithms also work with Euler's number and specifically they're called natural logarithms or natural logs for short. For example, Euler's number raised to the second power equals roughly 7.39. Raising Euler's number to an exponent is the same thing as raising approximately the base of 2.72 to an exponent. It's equal to one plus one divided by the factorial of n as it goes to infinity, which equals roughly 2.71828 or 2.72 if we want to round it to two decimal places. In logistic regression modeling, we won't be working with base 10 calculations, but instead we'll be working with one of the most important numbers in mathematics, Euler's number or E for short, which is a mathematical constant. For a base 10 logarithm on the number 1,000 the result is three, for example. A logarithm lets us solve for the exponent we want to put on the base of a number to get a certain result. Logarithms or logs for short, effectively work as a reverse of exponent. Let's say we're solving for the value of X, which equals the base of 10 raised to the third power, which gives us 1,000. I think that even if this isn't a new topic to you, it's well worth reviewing before we start creating our models. Along with statistics and probability, exponents and logarithms are two important concepts in logistic regression models.
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