solve 2x lnx + x = 0
THAT IS HARD WHAT GRAGE ARE YOU IN 100th!!!!
the sum of two #'s is 17. there product is 72. what are the 2 numbers?
To solve the equation 2x lnx + x = 0, we need to find the value(s) of x that satisfy the equation.
To start, let's rewrite the equation using the properties of logarithms. Recall that lnx = loge(x), where e is the base of the natural logarithm.
So, the given equation becomes:
2x loge(x) + x = 0
Next, let's isolate the logarithmic term by subtracting x from both sides of the equation:
2x loge(x) = -x
Now, we can divide both sides of the equation by x to solve for loge(x):
2 loge(x) = -1
Dividing both sides by 2 allows us to simplify further:
loge(x) = -1/2
Now, we can rewrite the equation using the exponential form of logarithms. The natural log function is the inverse of the exponential function. Therefore, if we write the equation loge(x) = -1/2 in exponential form, we get:
x = e^(-1/2)
We can simplify further by evaluating e^(-1/2):
x ≈ 0.6065
So, the approximate solution to the equation 2x lnx + x = 0 is x ≈ 0.6065.
To verify the solution, substitute the value of x back into the original equation and check if it holds true.