Equations like that will typically require the Lambert W function, also known as the product log function, and this is no exception. Your best bet right now is to find the solutions numerically.
For example, if you were given the line y = 3x and the logarithm y = log(x) + 5, to find the point(s) of intersection between them, you'd have to solve the equation 3x = log(x) + 5. I have no idea how to solve that for x.
Online graphing calculators show that there are actually two intersections in this example: (0.0001, 0.9897), (1.7475, 5.2424).
Is there an easy solution I'm missing, or do I need to learn something new (heaven forbid )?
Equations like that will typically require the Lambert W function, also known as the product log function, and this is no exception. Your best bet right now is to find the solutions numerically.
Thanks a lot--that's a great website (although it's worth mentioning that for some reason it handles log(x) as ln(x)--if you look at the bottom of the "Input interpretation" box it says "log(x) is the natural logarithm." Still got the answer right for 3x = ln(x) + 5, though).
EDIT: Nevermind ^^^ what's in parenthesis above, I didn't see that I just had to click something to change that.
Unfortunately I know very little about the Lambert W function. Any suggestions for a good explanation of it? (Wikipedia was a bit hard to follow, and I haven't even been to a pre-calc class yet, so I'm not surprised if there isn't). Thanks anyways :)
That reason is that Stephen Wolfram, the creator of Mathematica, which is the engine behind WolframAlpha, is a physicist. And physicists often write the natural logarithm as log.
The wiki is precisely where I would have pointed you first. You could also check out MathWorld's article.it handles log(x) as ln(x)--if you look at the bottom of the "Input interpretation" box it says "log(x) is the natural logarithm." Still got the answer right for 3x = ln(x) + 5, though).
Unfortunately I know very little about the Lambert W function. Any suggestions for a good explanation of it? (Wikipedia was a bit hard to follow, and I haven't even been to a pre-calc class yet, so I'm not surprised if there isn't). Thanks anyways
Okay...looks like I'm in over my head. I have a lot of trouble learning new material off websites as opposed to learning from teacher, so I'll wait to get a better understanding of this area in class. I was just curious about this and if I was missing some kind of algebraic way of solving it. Regardless, thanks for the help.
First define a new function f(x)=3x - log(x) - 5
And now...
try to understand: Newton's method - Wikipedia, the free encyclopedia