How do you solve equations like:
ln (x) = ax
where a is any positive whole number
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How do you solve equations like:
ln (x) = ax
where a is any positive whole number
You can't do it algebraically so you'd have to use the Newton-Rhapson method which goes something like this:
f(x) = ln(x) - ax
f'(x) = 1/x - a
xr+1 = xr - (ln(xr) - axr)/(1/xr - a)
Depending on the value of a, the equation f(x)=0 will have zero, one or two solutions. There's no foolproof way to find them other than sticking random numbers for xr into that equation to find the better approximation xr+1 until xr+1 converges to a specific value.