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### Course: Algebra (all content)>Unit 5

Lesson 8: Solving equations by graphing (Algebra 2 level)

# Solving equations graphically (1 of 2)

Sal solves the equation e^x=1/[x(x-1)(x-2)] by considering the graphs of y=e^x and y=1/[x(x-1)(x-2)]. Created by Sal Khan.

## Want to join the conversation?

• I don't get it... how is 7.846 and 7.633 within 0.01 ?
• Those are the values of E(x) and R(x). You want x within 0.01 of the actual value of x, not E(x) within 0.01 of R(x).
• At Sal uses his calculator and chooses "e" and raises that to a power of 2.1. What is "e" and where did that irrational come from?
• e is a constant, just like PI is a constant. e is something like: 2.71828.... e is the base of natural logarithm. I believe that e stands for Euler's number.
• I have never learned this stuff. are there videos before this that will help me do this?
• At the point Sal was looking for, the y values change enormously for tiny changes in x. Sal guesses a starting x of 2.1 by looking at the x axis. So would there be a way to use an estimate on the graph for the y axis, in order to go back and get a better starting point for the x value?
• If you used an inverse function for either R(x) or E(x) , then you could plugin an estimate of maybe 7.8 into that function, to come up with a starting value of x. e^x conveniently has an inverse function, which is ln(x).

ln(7.8) comes up as 2.05412373369554605284 on my calculator, which gives you a very good starting point, yes. :)
• What is the value of e at ?
• e is an irrational number like π (meaning it cannot be written as the ratio of 2 integers and thus in its decimal form it will go on forever without any pattern). The first few digits of e are:
e ≈ 2.718
• What is "e"? I've run into it, and I know it's aprox. 2.71812, but what is it's specific "job" in mathematics?
• The number represented by the variable 'e' is called Euler's Number. In math, it represents the base for something called the natural logarithm, which is a process that counteracts something being raised to a power, much like addition counteracts subtraction.
• Please, how exactly is E(x)=R(x) within 0.01 ?
• When it's much closer than either 2.05 and 2.07.
(1 vote)
• I seems that the correct Algebra way to solve this would be to subtract e^x from 1/(x(x-1)(x-2) and set it equal to zero. i.e. 1/(x*(x-1)*x-2))-e^x=0. This is actually kind of what I did in Excel. I just made two rows of formula and subtracted the results. If I knew how to solve for x with that natural log (e) that is exactly what I would do.
• the solution suggested by jeffery works well
log natural in excel is ln()
charting in excel is as good as a calculator