The triangle that helps you solve mathematical operations

The triangle that helps you solve mathematical operations

The math! That subject that you either love or hate!

I personally loved them, but I must admit that some termsthey were quite difficult to assimilate when they were first given.

Limits, derivatives, integrals Simply hearing his name was enough to bristle the hair of more than one student, but even some simpler concepts got stuck if the teacher couldn’t find an easy way to explain it. This is the case of the logarithms, those operations that had something to do with the powers, but whose understanding is often resisted. Well, what if I told you that they can be assimilated with a simple triangle? Yes, yes, you read correctly. A triangle! They tell us in a video from the YouTube channel 3Blue1Brown and we will explain it to you too, in case you don’t feel like following the video.

What are logarithms?

Okay, before we start talking about this triangle, baptized as the power triangleLet’s do a little review of basic mathematics to understand what the logarithm resolution.

The logarithm is composed of a small subscript number and a larger onecalled base and argument respectively. But what do they have to do with each other?

Well, basically, that the logarithm solution is the number to which the base must be raised to obtain the argument. I explain.

Imagine we have the logarithm to base 2 of 8 (log28). In this case, the solution will be the number to which you have to raise two (base) to get 8 (argument). And that number what is it? Well, 3, because 2 = 8.

How are roots resolved?

Another operation related to powers is the root; since, in fact, it is exactly the opposite. In the same way that the opposite of the sum is the subtraction and that of multiplication is division, that of the powers is the root.

Thus, if 2 = 8, we can affirm that 8 = 2

Okay, that’s all very well, but when it comes down to it, it’s very easy. confuse concepts, so a little trick, like the one we are going to teach you today, can be the difference between rolling it on an exam or getting an outstanding one.

What is the triangle of power necessary for solving logarithms?

This figure is but a mathematical curiosity, but I know that it is true that it is useful when making simple operations.

Like every triangle, it has three vertices, in which the three parts of a power are placed from left to right. Therefore, if we know that 2 = 8, we will place it as follows.

And once the numbers are in place we can solve both roots and logarithms associated as shown in the image.

Logically, the solution to the logarithm and root will be the missing vertex, so the logarithm solution will be 3 and the cube root solution will be 2.

More examples appear in the video at the top, but I encourage you to substitute the numbers yourself to verify that the rule is indeed being followed in all cases.

Okay, when we did the logarithms in high school the exercises were not so simple, but even so this triangle would have been very useful to us in the beginning, don’t you think?

Images: Educational portal Cuba Educa

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