-𝔏𝔲𝔪𝔦𝔫𝔢𝔰𝔠𝔢𝔫𝔱 ||Jikook||

Numbers

"What was that dream?"
🏮🏮🏮🏮𝔏𝔲𝔪𝔦𝔫𝔢𝔰𝔠𝔢𝔫𝔱🏮🏮🏮🏮

Jimin looked up to Taehyung with a rather spiteful expression lying on his face, annoyed at being woken up. Taehyung rolled his eyes like the sassy boy he was and walked out of the room for Jimin to start getting ready.

The boy sluggishly got up out of his bed and put on his black uniform, white tie and ID. He styled his hair a tad bit and walked downstairs where Taehyung was.

"We can eat at the food court once we get there so get your shoes on and your bag so we can leave," Taehyung exclaimed before grabbing the treats out of the refrigerator and unlocking the door.

Jimin reluctantly put on his shoes and took his bag, catching up with Taehyung at the door, then both of the boys left for the school.

"Trust me Jimin, I don't want to go to school at the moment either, so stop complaining about it and let's just deal with it." Taehyung sighed looking at Jimin, the boy nodded and looked ahead of their path. The school was close, but not at the same time; they had to cross through the shopping district of the campus and the food court.

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"Hey Jimin, you're spacing out again," Yoongi sighed, still not able to get his attention. The truth is, Jimin couldn't stop thinking about JeongGuk. He was always in the blonde's mind throughout the day already.

Once Taehyung slapped Jimin on the shoulder, he finally came back to reality, squealing some after the impact. Jimin looked over to Taehyung and gave him a pained expression, Jimin never liked being hit, but it always helped him get out of his thoughts.

Jimin slouched down in his chair and looked up at the ceiling, wanting the bell to ring so he could get to lunch quicker. To his liking, the bell rang and the students got quiet and stood up.

To everyone's surprise, it wasn't their normal Teacher Nicholas; instead, it was a young woman. Despite that, all the students bowed and continued to greet the Teacher.

She smiled and bowed back, "Hello class, for now on I am your Teacher; your former Teacher apparently was on drugs so... good for you guys," she chuckled a bit and sat down on her desk.

"My name is Φωτεινή or Fotini if you prefer that, I know most of you students in this class don't even speak Greek. I really don't care about formalities, and even though I'm going to make your life hell by teaching you a subject that none of you will use in your lifetime, treat me as a friend; I am only 3 or 2 years older than most of you." Fotini stated and stood up.

The class started talking to each other, surprised at the new teacher's lax attitude. Other teachers are very strict but in all honesty, Jimin believed he would enjoy this class more. Once the bell rang again, the students sat down and looked at Fotini, waiting for her to start.

Fotini pushed her blonde hair back and took out a marker, "Once we get this lesson done, we can do a few entertaining things."

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"Once you are familiar with and, you can look at logarithmic functions. Logarithms are basically another way of writing and logarithmic functions are inverses of exponential functions.

An important definition that we should keep in mind is the definition of logs because it will help tremendously when dealing with logarithmic functions and various types of log problems.

To reiterate, a logarithm is another way of writing an exponent. This definition works in both directions (converting from exponential form to logarithmic and back). The domain for logarithmic functions will be all positive real numbers for x and the range will be all real numbers for y.

When we write log(x) without a base, it is understood that the base is 10. On a calculator, there are two types of logs, a base ten log and the natural log ln(x). The natural log is of base e, which we found is a unique exponential function. Many problems will deal with e and we will have to use the natural log ln to evaluate and graph the function.

Graphing the exponential function and natural log function, we can see that they are inverses of each other.

Let's graph the function f(x) = log(x+2) of base 4.

We can then plug in values for y and yield our x values. Though we usually plug in x values to find our y values, it is much easier in this form to plug in various values for y.

Notice that now we have a vertical asymptote at x = -2, and a point at (-1,0). This is exactly the opposite of exponential functions, which have horizontal asymptotes and a point at (0,1). All logarithmic functions will have a vertical asymptote and pass through the point at distance 1 from the vertical asymptote in the direction it opens up. This point will always be the x-intercept. To find it, we can set y equal to 0 and solve for x.

Let's look at the graph of f(x) = ln(5-x)."

Fotini takes a deep breath and stops, "Screw this, you all know this so everyone get on your laptops, I got steam unlocked." Many in the class cheered in excitement and all Jimin could do is just look to Taehyung confused.

They were supposed to be doing Pre-Calculus, but somehow the entire class was playing games, and the Teacher was too.

Taehyung just shrugged and got on his computer with Yoongi and Jin, leaving Jimin there kinda doing nothing. He thought, if the teacher was allowing them to do this, he could get away with sleeping.

He lied his head down and closed his eyes, all the commotion was drained out and it was utter silence for the young boy.

Soon after, he opened his eyes to the same landscape; the same beautiful valley, the same populated area, everything was the same.

Jimin slightly feels a weight on his shoulder and looked towards its direction.

"Welcome back."