Solve for x: e^x - 15e^-x = 2 | Algebraic Solution & Step-by-Step Guide

Thread starter Webs993
Start date Jan 21, 2009

In summary, solving for x in this equation allows us to find the value of x that satisfies the equation and can be used to find other important information or relationships. This equation can be solved algebraically by factoring and applying basic rules and properties of exponents and logarithms. The first step in solving this equation is to combine like terms by factoring out e^-x. There are restrictions on the possible values of x, as e^x and e^-x can only take on positive values. The significance of the solution(s) is that they represent the value(s) of x that make the equation true and can help us understand the relationship between the two exponential functions and solve related problems.

Jan 21, 2009

Webs993

im having a problem solving this problem algebraically please help thanks

e^x - 15e^-x = 2

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Jan 21, 2009

praharmitra

put e^x = y. And then solve for y

Jan 21, 2009

Mentallic

Homework Helper

Remember the rule: [tex]a.b^{-c}=\frac{a}{b^c}[/tex]

You will have a quadratic in [tex]e^x[/tex]

1. What is the purpose of solving for x in this equation?

The purpose of solving for x in this equation is to find the value of x that satisfies the equation and makes it true. This value can then be used to find other important information or relationships in the given problem.

2. Can this equation be solved algebraically?

Yes, this equation can be solved algebraically by applying basic rules and properties of exponents and logarithms.

3. What is the first step in solving this equation?

The first step in solving this equation is to combine like terms by factoring out e^-x from the left side of the equation. This will result in a quadratic equation in terms of e^x, which can then be solved using the quadratic formula.

4. Are there any restrictions on the possible values of x in this equation?

Yes, there are restrictions on the possible values of x in this equation. Since e^x and e^-x are both exponential functions, they can only take on positive values. Therefore, any value of x that results in a negative value for either e^x or e^-x is not a solution to the equation.

5. What is the significance of the solution(s) to this equation?

The solution(s) to this equation represent the value(s) of x that make the equation true. This can be helpful in understanding the relationship between the two exponential functions and can also be used to solve other related problems or equations.