Not a nitpick at all, it's something I do need to have. I just gave a briefer version here to save on the amount of time it takes me to post. Excellent advice though, and I agree with you completely.
I see why $$log_{b}b$$ cancels, but it's not clear to me (unless using the exponent rule) that...
He did say "left side," and my left side was $$log_{b}(b^{u+v}).$$ The right side $$log_{b}x+log_{b}y$$ can be simplified into $$u+v$$ by the fact that $$log_{b}x=u,log_{b}y=v,$$ (which I embarrassingly overlooked) but then that would leave me with $$log_{b}(b^{u+v})=u+v.$$
Thanks again,
Joe
How does the left side simplify to that? If I'm not mistaken, you've used the exponent property which states $$log_{b}b^{a}=a*log_{b}b=a*1=a,$$ which, as I've said, I cannot use because I've not proven that yet. Furthermore, in my proof of that exponent property, I use the product of logarithms...
Homework Statement
Prove that $$log_{b}(xy)=log_{b}x+log_{b}y.$$
Homework Equations
Let $$b^{u}=x,b^{v}=y.$$ Then $$log_{b}x=u,log_{b}y=v.$$
The Attempt at a Solution
I'm afraid I've been using circular reasoning to prove this. I can get this to a point where I have...
Thanks for the reply and the feedback! A few replies from me...
1.) That's a great suggestion. I hint at this idea subtly in the exercises, but it certainly could use some more attention. It also wouldn't add that much tangential (no pun intended) material.
2.) Agreed on this point. My...
Good morning everyone,
I have written a free math textbook, and I'd appreciate some feedback on it. It's about the basics of Trigonometry, including sine, cosine, tangent, radians, the unit circle, a bit on identities, and the Law of Sines, Cosines, and Tangents. I wrote it in a rigorous...
1. The problem statement, all variables and given/known
Find the length of the curve $$y=ln(x),\frac{1}{2}<=x<=2$$
Homework Equations
Using hyperbolic trig isn't necessary, but it's how my text (Serge Lang's A First Course in Calculus) approaches most square roots, and as a result, it's what...
I have a question regarding the double slit experiment. I have been doing a little reading (The Grand Design, to be specific) and I was left with a burning question.
First of all, I am not a physics major. I have taken only one college physics class, and although it is something that...