Find x: Solving Equations for x in y=2/x and y=e^(x-4)

Thread starter TyErd
Start date Feb 22, 2010

In summary, to solve for x in y=2/x, you can multiply both sides by x and then divide by y to get x=2/y. To solve y=e^(x-4), you can take the natural logarithm of both sides and then add 4 to isolate x, giving you x=ln(y)+4. These equations can be solved using a scientific calculator by using functions such as reciprocal or natural logarithm. In real-life scenarios, y=2/x represents an inverse relationship between two variables while y=e^(x-4) represents exponential growth or decay. Other methods for solving equations include substitution, elimination, and graphing, but the methods mentioned above are the most common and efficient for these specific equations.

Feb 22, 2010

TyErd

find x.

y=2/x
y=e^(x-4)

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Feb 22, 2010

HallsofIvy

Science Advisor

Homework Helper

TyErd said:

find x.

y=2/x
y=e^(x-4)

2/x= e^(x-4)= e^x e^(-4)

2= x e^x e^(-4)

xe^x= 2e^4

x= W(2e^4) where W is Lambert's W function:
http://en.wikipedia.org/wiki/Lambert_W_function

which is defined as the inverse function to xe^x.

1. How do you solve equations for x in y=2/x?

To solve an equation for x in y=2/x, you first need to isolate the variable x on one side of the equation. In this case, you can do this by multiplying both sides of the equation by x. This will cancel out the x on the right side, leaving you with yx=2. Then, you can divide both sides by y to isolate x and get the final answer of x=2/y.

2. What is the process for solving y=e^(x-4)?

To solve y=e^(x-4), you can take the natural logarithm (ln) of both sides of the equation. This will cancel out the e and leave you with ln(y)=x-4. Then, you can add 4 to both sides of the equation to isolate x and get the final answer of x=ln(y)+4.

3. Can I solve these equations using a calculator?

Yes, you can solve these equations using a scientific calculator. Simply input the equation and use the appropriate function or key to solve for x. For example, to solve y=2/x, you can use the reciprocal function on your calculator to get x=2/y. For y=e^(x-4), you can use the natural logarithm function to get x=ln(y)+4.

4. What do these equations represent in terms of real-life scenarios?

The equation y=2/x represents an inverse relationship between two variables. For example, if y represents the cost of an item and x represents the quantity purchased, this equation shows that as the quantity increases (x), the cost decreases (y). The equation y=e^(x-4) represents exponential growth or decay, where x is the independent variable and y is the dependent variable.

5. Are there any other methods for solving these equations?

Yes, there are many different methods for solving equations, such as substitution, elimination, or graphing. However, the methods mentioned in the previous questions are the most common and efficient for solving y=2/x and y=e^(x-4). It is always important to choose the method that best suits the specific equation and problem at hand.