Recent content by Aphex_Twin

whoops, I miswrote b as n somewhere on the mid way. a^x+x^b=c a^x = c - x^b x*ln(a) = ln(c - x^b) x = ln(c-x^b)/(ln(a)) x = ln(c-x^b) * (1/(ln(a))) 1 = ln(c-x^b) * (1/ln(a)) * 1/x ln(a) = ln (c - x^b) * 1/x ln(a) = ln(c-x^b)*e^(-ln(x)) (ln(a))^b = (ln(c-x^b))^b*e^(-ln(x^b))...

Eureka! a^x+x^b=c a^x = c - x^b x*ln(a) = ln(c - x^b) x = ln(c-x^b)/(ln(a)) x = ln(c-x^b) * (1/(ln(a))) 1 = ln(c-x^b) * (1/ln(a)) * 1/x ln(a) = ln (c - x^b) * 1/x ln(a) = ln(c-x^n)*e^(-ln(x)) (ln(a))^n = (ln(c-x^n))^n*e^(-ln(x^n)) (ln(a)^(n*ln(-1)) =...

I'm looking into it and it's very interesting. Please correct me if my calculations are wrong. I start with a simpler equation, namely: x=2*ln(x) e^x = x^2 1 = x^2/e^x 1 = x^2 * e^(-x) 1 = x * e^(-x/2) -1/2 = -x/2 * e^(-x/2) Therefore x = W(-1/2) So going ahead with the main...

There must be something I'm missing, or unknowing of, that I reach a dead end: a^x + x^b = c x^x = c - x^b x*ln(a) = ln(c - x^b) x = ln(c-x^b)/(ln(a)) x = log_a (c-x^b) ?? where log_a is the base-a logarithm

How does one proceed to solve an equation of the form: a^x + x^b = c Where x is the unknown (real or complex) and a, b, c real constants. Or at least if you know a line of attack.

Given n, can we find a triplet a, b, c that fits the following conditions: n = a*b+c+5 abs(a-b+c) is minimum but only if n>a+b+abs(c)+5 Where n, a, b are naturals and c is integer. For instance in case of n=65, I have a hunch the best choices are: a = b = 8 c = 1 The...

What is the energy required to heat up one H2 and one H3 from a given temperature n (Kelvin), up to 10^9 K (required for fission)? How does the density of an object bound solely by it's gravitational compression and electron repulsion vary? My guess is that it should be cubic or...

If you have 1 kg of matter, what is the energy equivalent of it in say joules? How much of the matter (heavy hidrogen?) that goes into a fusion reaction is transformed to energy? And to the point... Last year there was this discussion about what would happened if the Galileo orbiter...

If we pass a ray of white light through a red piece of plastic (filter), the outcome will be red light, but the light would not be essentially diferent, only at a reduced number of wavelengths. Can someone explain how is the polarization filter diferent (in acting like a "measurement device")?

What if the string had negligible mass, but would be strong enough not to break and the bullet had mass, but would not get untied from the rope. The string is also tied to something. As the bullet travels it will draw the string behind it. When the bullet has traveled the length of the string...

I was thinking of something: Say we have pairs of entangled photons. Say we send these through a polarization filter. We can call the output "ones". Now, we separate the pairs into two streams (through two optic cables). We store one member of the pair (without measuring it) and send the...

Well, you could represent $62.56 as $63 and $-0.44 (your error), as 2 separate cells. You constantly add up the current error with the previous one and when it gets to $5 you take it into consideration.

You mean to "round" to the nearest number multiple of 5. It's easy: =int(your_cell/5)*5 [+or not 5] You check the value of int(your_cell/5)*5 and that of int(your_cell/5)*5+5 and with an if function calculate which diverges the least and chose that.

Alright, I'm getting it. I presume there are more such "branch cuts" to be made when talking of quaternionic powers of quaternions. This means for quaternions I can use the formula for complex exponentiation, replace the real numbers with complex numbers (chosing an appropriate norm and atan...

What if I make r and t dependent on a c and d, where p=c+d*i r = |p| = sqrt(c^2 + d^2) t = arg (p) = atan(d/c) This way there is a unique representation. I'm looking more into it... I was also looking at the formula here: http://mathworld.wolfram.com/ComplexExponentiation.html And...