To solve for x in this equation, we can use logarithms. Taking the natural logarithm of both sides, we get ln(ex) = ln(1/x). Using the properties of logarithms, this simplifies to x = 1/e.
The solution x = 1/e represents the value of x that satisfies the equation, meaning when x is substituted into the equation, it will result in the equation being true. It is the exact value of x where the graph of ex and 1/x intersect.
Yes, there are infinitely many solutions for this equation. In addition to x = 1/e, there are also negative solutions for x. These values can be found using complex numbers, but in the context of real numbers, x = 1/e is the only solution.
Yes, there are other methods for solving this equation without using logarithms. One method is to graph both ex and 1/x and find the point of intersection. Another method is to use approximations, such as using a calculator or estimating the value of x.
This equation has many practical applications in mathematics, physics, and engineering. For example, it can be used to model growth and decay in various systems, such as population growth or radioactive decay. It is also used in calculus to find the slope of a tangent line to a curve at a specific point.