Mastering the Mysteries of Logarithms: Solving for x in a Tricky Equation

Thread starter DeanBH
Start date May 12, 2008

May 12, 2008

DeanBH

i've got a logashizm problem to this point

the log is base 2log (x(x+3)^2 / (4x+2)) = 1

apparently x(x+3)^2 / (4x+2) = 2

no idea why, halp?

thxgod damn it, nvm

2^1 = (x(x+3)^2 / (4x+2)) when you take the damn log out.

Last edited: May 12, 2008

Physics news on Phys.org

May 12, 2008

BrendanH

exactly

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...

View full post »

Thread 'Making the denominator of a certain fraction real'

Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...

View full post »