Finding roots of an exponential equation

Thread starter Akash47
Start date Nov 1, 2019
Tags

Exponential Roots

In summary, the roots of an exponential equation can be found by setting the equation equal to zero and solving for the variable using logarithms. Not all exponential equations have roots, as some may have no real roots or complex roots. The difference between a root and a solution is that a root makes the equation equal to zero, while a solution makes the equation true. There are special techniques for finding roots of exponential equations, such as using logarithms, graphing, or iterative methods. An exponential equation can have multiple roots, but if the base is positive, there can only be one positive and one negative root.

Nov 1, 2019

Akash47

Homework Statement: Given that f(x)=(3^x).(e^x).(x^2-4) for real x.Find the root of the function.(setting f(x)=0).

Relevant Equations: No equations required.

I know that both 3^x and e^x can't be 0 for real x. Then x^2-4=0 is the only choice and we get x=2,-2. Am I right? Or should I add something?

Physics news on Phys.org

Nov 1, 2019

Delta2

Insights Author

Gold Member

yes you are right

Nov 1, 2019

Akash47

Thanks

1. What is an exponential equation?

An exponential equation is an equation in which a variable appears in an exponent. It has the general form y = ab^x, where a and b are constants and x is the variable.

2. How do you find the roots of an exponential equation?

To find the roots of an exponential equation, you need to set the equation equal to zero and solve for the variable. This can be done by taking the logarithm of both sides of the equation or by using algebraic methods.

3. Can an exponential equation have more than one root?

Yes, an exponential equation can have multiple roots. The number of roots depends on the value of the exponent and the values of the constants in the equation. For example, an equation with an even exponent will have at least two roots, while an equation with an odd exponent may have only one root.

4. How do I know if a root of an exponential equation is real or complex?

If the exponent in the exponential equation is an even number, then all of the roots will be real. However, if the exponent is an odd number, then there is a possibility that some of the roots will be complex numbers. To determine if a root is complex, you can use the discriminant formula.

5. Can an exponential equation have irrational roots?

Yes, an exponential equation can have irrational roots. This means that the roots cannot be expressed as a fraction of two integers, and they are usually expressed using square roots or other irrational numbers. For example, the equation y = 2^x has an irrational root at x = 0.693147... (which is the natural logarithm of 2).