ln(x) + 2^x = 3
is there any way to calculate this with pen and a paper or do you have to use a computer to approximate it?
>>7673521
That's a function, you don't have to calculate anything.
>>7673529
But there's only one variable.
>>7673529
>That's a function
No, this is an equation. It is only valid for one value of x.
>>7673521
Use Newtons method, but do it by hand.
>>7673533
equations can have more than one solution, lel.
>>7673533
sin(x) = 1
What is the value of x?
>>7673542
Kek
>>7673521
You won't get exactly 3 but you can do this with functional approximation using derivatives and integration. Approximate ln(x) and 2^x using polynomials - depending on what x value you're looking for, you would want to approximate the slope at a known x value around that point.
>>7673521
>>7673521
There is one solution....
http://www.wolframalpha.com/input/?i=ln%28x%29+%2B2%5Ex%3D3
o.o I also rearranged it to
xe^(2^x)=e^3 to see if I can simplify it, but that one goes out of control just as fast when taking the derivative. -.-
http://www.wolframalpha.com/input/?i=xe%5E%282%5Ex%29%3De%5E3
Wolfram choked on itself a little when calculating either...XDDD
Product log forms are fun.
>>7673521
I'd suggest Newton's Method. Takes too long to do though. Just use a program.
