# Logarithms in Systems of Equations

• Mandelbroth
However, numerical methods such as finding the point of intersection can be used to approximate the solutions. In summary, finding the solution set for the system of equations y=e^{-x}+1 and y=2+lnx does not have a simple algebraic approach and may require the use of numerical methods for approximation.
Mandelbroth

## Homework Statement

Consider the system...

$y=e^{-x}+1 \\ y=2+lnx$

## The Attempt at a Solution

I don't think there is a "pretty way" (algebraic manipulation) to do this. I simply found the point where the plots intercepted, getting the solution set (0.62745018..., 1.5339409...).

Is there a better way to do this? For what it's worth, this was for a friend who claims that her math teacher is unreasonable, so I don't know if it does has a fully algebraic approach.

Edit: For clarity, both have a domain and codomain in the set of real numbers, so there isn't an imaginary part to worry about.

Last edited:
Mandelbroth said:
Is there a better way to do this?
In general, there is not. Some equations have an analytic solution which is easy to find (x+e^x = 1 for example), but the general case does not have a nice solution.

## 1. What are logarithms in systems of equations?

Logarithms in systems of equations are mathematical tools that are used to solve equations involving exponential functions. They help to simplify complex equations and make them easier to solve.

## 2. How are logarithms used in systems of equations?

Logarithms are used in systems of equations to transform exponential equations into linear equations. This makes it easier to solve for the unknown variables and find the solutions to the system.

## 3. What is the purpose of using logarithms in systems of equations?

The purpose of using logarithms in systems of equations is to make solving complex equations more manageable. They help to simplify the equations and make it easier to find the solutions.

## 4. Can logarithms be used to solve any type of system of equations?

Yes, logarithms can be used to solve any type of system of equations. They are particularly useful when the equations involve exponential functions, as they help to simplify the equations and make them easier to solve.

## 5. Are there any limitations to using logarithms in systems of equations?

While logarithms can be very helpful in solving systems of equations, there are some limitations. They may not be the most efficient method for solving certain types of equations, and they may not work for every equation. It is important to understand when it is appropriate to use logarithms in a system of equations.

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