Authentic voices. Remarkable stories. AOL On Originals showcase the passions that make the world a more interesting place.
EMMY NOMINATED SERIES directed by and starring Steve Buscemi is back for a second season!!! Park Bench is a local's take on the special people, places, and spirit of New York City. Through unscripted moments with average New Yorkers and Steve's celeb friends, Buscemi takes viewers on a funny, first-hand journey/misadventure, told in his unique voice.
Journey to the Draft is an organic, unscripted, docu-series that follows three college football players, all with promising professional careers. These young men attend different schools across the country and play a variety of positions on the field, but at the end of the day they share one goal:to play in the NFL. The AOL docu-series follows players Leonard Williams, Kevin White and Marcus Peters.
Connected features the personal stories of six New Yorkers woven together into one of the most intimate series ever. This groundbreaking show changes the nature of storytelling by giving each character a camera to document their lives. The result is a unique format revealing as different as everyone appears to be, we are all universally Connected.
Wake up to your world in 2 minutes.
"Stricly Come Dancing presenter Tess Daly and The Saturdays' Rochelle Humes talk to mums about their experiences of being mum. Whether the daughter of a Rolling Stone, in one of the most famous girl bands the world has ever known, or a parent coping with disability as well as family life, each mother in Being Mum shows that the feelings, challenges and rewards of motherhood are universal no matter the surroundings you find yourself in."
Jews and Money. Asian Drivers. Polish IQ. CPT… that's racist! But where do these stereotypes come from? Comedian Mike Epps explores the backstories of this humor and how history and fact often distorts into a snide – but sometimes funny – shorthand.
"INSPIRED" features celebrities, visionaries and some of the biggest newsmakers of our generation, recounting the stories behind their biggest, life-changing moments of inspiration.
In a compelling series of verite encounters, Win Win provides unique access into the minds and lives of the world’s most-celebrated entrepreneurs and athletes.
Explore what it means to be human as we rush head first into the future through the eyes, creativity, and mind of Tiffany Shlain, acclaimed filmmaker and speaker, founder of The Webby Awards, mother, constant pusher of boundaries and one of Newsweek’s “women shaping the 21st Century.”
Nicole Richie brings her unfiltered sense of humor and unique perspective to life in a new series based on her irreverent twitter feed. The show follows the outspoken celebrity as she shares her perspective on style, parenting, relationships and her journey to adulthood.
Comedy is hard, but teaching comedy to children is hilariously difficult. Kevin Nealon is giving the challenge to some world-famous comedians. As these young minds meet with comedy’s best, get ready to learn some valuable comedy lessons, and to laugh!
James Franco loves movies. He loves watching them, acting in them, directing them, and even writing them. And now, he’s going to take some of his favorite movie scenes from the most famous films of all time, and re-imagine them in ways that only James can.
The story of punk rock singer Laura Jane Grace of Against Me! who came out as a woman in 2012, and other members of the trans community whose experiences are woefully underrepresented and misunderstood in the media.
Hello! Let’s do some work on logarithm properties. So let’s just review real quickly what a logarithm even is. If I write log base x of A is equal to N, what does this mean? Well, this just means that x to the N equals A. I think we already know that, we’d learned that in the logarithm video. It’s very important to realize that when you evaluate a logarithm expression like log base x of A, the answer or when you evaluate what you get is an exponent. This N is really just an exponent; this is equal to this thing. You could have written just like this because this N is equal to this. You could just write x to the log base x of A is equal to A. All I did is I took this N and I replaced with this term. And I wanted to write it this way because I want you to really get an intuitive understanding of the notion that a logarithm when you evaluate it, it really is an exponent. And we’re going to take that notion and that’s where really all of the logarithm properties come from.
What I actually want to do is I want to stumble upon the logarithm properties by playing around it then later on I’ll summarize them and clean them all up. But I want to just show maybe how people originally discovered this stuff. So let’s say that x to the L is equal to A. Well if we write that as a logarithm, that’s same relationship as a logarithm, we could write that log base x of A is equal to L. If I were to say that x to the M is equal to B and the same thing, I just switched letters but that just means that log base x of B is equal to M. I just did the same thing that I did in this line, I just switched letters. So let’s just keep going and see what happens.
Let’s say I have x to the N is equal to A x B and that’s just like saying that log base x is equal to A x B. So what can we do with all of this? Well let’s start with this right here, x to the N is equal to A x B. So how can we rewrite this? Well A is this and B is this, so lt’s rewrite that. So we know that x to the N is equal to A, A is this, x to the L. And what’s B, times B, well B is x to the N. What x to the L times to the L? Well we know from the exponents when you multiply two expressions that have the same base and different exponents you just add the exponents. So this is equal to, when you have the same base and you’re multiplying, you can just add the exponents, that equals x to the L+M. So x to the N is equal to x to the L+M. Well we have the same base these exponents must equal each other. So we know that N is equal to L+M, and what does that do for us? What’s another way of writing N? So we said x tot eh N is equal to A x B that means that log base x of A x B is equal to N.
Anyway, so what’s N? What’s another way of writing N? Well another way of writing N is right here, log base x of A x B. Now we know that if we just substitute N for that we get log base x of A x B and what is that equal? That equals L, and another way to write L is right up here. It equals log base x of A+M, and what’s M? M is right here, log base x of B. And there we have our first logarithm property. The log base x of A x B well that just equals the log of base x of A plus the log base x of B. And this is hopefully, this proves that to you and if you want the intuition of why this works out it falls from the fact that logarithms are nothing but exponents.
So with that, I’ll leave you with this video and in the next video I will prove another logarithm property. I’ll see you soon.
Comments