What is the power I need to raise b to to get to four. Now let's look over here, when x is equal to four The line, y is equal to x and this is clearly In general when you're taking an inverse you're going to reflect over Notice this pointĬorresponds to this point, we have essentially
We have the point one comma zero, so it's that point over there. If we assume that b is non zero and that's a reasonable assumption because b to different What is y going to be here? y is going to be log base b of one. Let's take these values because these areĮssentially inverse functions log is the inverse of exponents. What are the possibilities here? What I want to do is think. Now it's essentially the inverse function where this is going to be x and we want to calculate y Three corresponding points on this function. When x is equal to two, b to the second power, y is equal to 16. That b to the second power is equal to 16. Another way of thinking of this y or four is equal to b to the first power and actually we can do When x is equal to one, b to the one power or b to the first power is equal to four. What is this first function? This first function is telling us so x, and this is y isĮqual to b to the x power. I've actually copy and pasted this problem on my little scratch Based only on these three points, plot the three corresponding points that must be on the graph of y is equal to log base b of x by clicking on the graph. Voiceover:The three points plotted below are on the graph of y isĮqual to b to the x power. Since we have calculators that can do this math for us, it is possible for people to use logs without having to master very advanced and difficult computations.īut, just for reference, here is one way to write the actual definition of a logarithm So, the reason you are not given exactly what a log is or how to compute it by hand at this level of study is that it is very difficult math. Thus, by definition, the log must be the inverse function of the exponential function. So, a log is just a quick way of writing the inverse function of an exponential function. The term "log" is just a shorthand way of expressing this difficult bit of math. In other words, there is a difficult mathematical process that was worked out over the course of about 80 years by Nicholas Mercator, Leonhard Euler and others. The actual definition of a logarithm that proves this is several years ahead of the math you're having now, so it wouldn't mean much to you at this stage.īut, the short answer is that the logarithm was invented to be the inverse operation of an exponential function.
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