How to solve? ln(x)=2/x-2
1 Answer
Consider properties of the two sides of the function and deduce the number of possible roots
Explanation:
As this equation has the variable both inside and outside of the logarithm, it does not have an analytic solution in terms of simple functions. So we must deduce properties rather than simply solve.
Consider the behaviours of the two sides of the equation along the real line.
For positive
In general, solving this type of problem requires numerical approximation. However, in this particular example, trialling some simple values immediately delivers us the answer:
Sanity check this by overplotting the two sides of the equation and observing where they cross:
graph{(y-ln(x))(y-(2/x-2))=0 [-10, 10, -5, 5]}