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Have you wondered why numbers float? What is an exponent any way? Why is an exponent also called an Index? What's all this powers stuff? Well, this video is here to demystify the mysterious worlds of index laws and exponents. OK. I call them floaty numbers as they are numbers what float! Every one else calls them indices. You say potato and I say ... well ... potato to be honest. In this video I take a look at how to multiply terms with indices, divide terms with indices, explain that the zero index is and why it is always one. I look at the product rule and the quotient rule all within about 15 minutes. If you want to know everything there is to know about powers/indices/indexs'/floaty numbers ... then watch the video!
This video looks what it means to solve equations by firstly looking at the graphical method. It looks at what a quadratic is and how to solve it when it equals 0 and other numbers. With this awesome information at hand, I move on to look at exponential equations and show how we can use the work we have already been doing on powers/indices/floaty numbers to solve these equations. Whilst they look hard - they really aren't! I finally take a look at how we can solve exponential equations which use inequalities.
Say the word Logarithms to anyone over the age of 40 and they will run away screaming. Why ... well .. they would remember the days of Log Tables. Before calculators, they had to use massive books of Log values to try and solve the most basic of questions. Thankfully, things have moved on and we now have calculators. But, Logarithms are still really important to us. This video looks at how Logarithms are related to graphs of exponential functions as well as how we can use Logarithms to change really large scales (on graphs) into more readable values. Moving onto the Logarithm rules there are lots of examples of how to use each of the rules to simplify and evaluate logarithms. This video is everything you need to help you understand this really important topic.
We have looked at the concepts of what exponential graphs are and how we can draw them. We have looked at how we can simplify them and now it's onto the exciting stuff to see how we can solve exponentials and graphs. I open the video with a small rant about how people who do nothing more than fly the world recording videos about them eating food can get 3.2 million views in 3 days! Yet I am here doing all I can to educate the world and have 3.2 views LOL. I then move onto showing you ... not one, not two but three different ways of looking solving exponentials to find the values of x. This includes the idea of a change of base. This theory is then used to show how to solve inequalities and sketch graphs of exponentials. Who would have thought that solving exponential graphs could be this much fun!
This graph completes the section on Logarithms and Exponentials. It opens by looking at the relationship between exponentials and logarithms. It recaps some of the concepts behind inverse functions and applies them to the graph of exponentials logarithms. Diving into the fun which is algebra, I then look at how we can find the inverse of an exponential function and a logarithm function. Finally, I look at how we can find the domain and range of an inverse function by finding the domain and range of the original function. A number of examples are covered before the video concludes.
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These are the videos which are available in each chapter. You will notice that some are free and some are for subscribers only. Making and hosting these videos costs a little bit of money. To help pay for the hosting fees I have no choice but to hide some of the videos and make them for subscribers only.