I'm not sure how to solve this problem, but the answer's -12
e^(x-6)=(1/e^2)^(X+6)
Thanks :D
The right hand side can be transformed to (e^-2)^(x+6)
=e^(-2(x+6))
Now both left- and right-hand sides are to the base e, you can take the natural logarithms of each side.
Using ln(e^y)=y, you will end up with a linear equation with x as the unknown.
I do not get -12 as the solution of x.
You can post what you get for checking.
A nurse wants to add water to 38 ounces of a 10% solution of benzalkonium chloride to dilute it to an 8% solution. How much water must she add? (Hint: Water is 0% benzalkonium chloride.)
To solve the equation, e^(x-6) = (1/e^2)^(x+6), we can start by simplifying the expression on the right-hand side.
Recall that (a^-n) = 1/(a^n), so we can rewrite (1/e^2) as e^(-2).
Now the equation becomes e^(x-6) = e^(-2(x+6)).
To solve this equation, we can equate the exponents and solve for x:
x - 6 = -2(x + 6)
Let's simplify the equation:
x - 6 = -2x - 12
Next, let's group all the x terms on one side and all the constant terms on the other side:
x + 2x = -12 + 6
Combining like terms:
3x = -6
Finally, divide both sides by 3 to obtain the solution for x:
x = -6/3
Simplifying further:
x = -2
Therefore, the solution to the equation e^(x-6) = (1/e^2)^(x+6) is x = -2.
To recap the steps:
1. Simplify the expression on the right-hand side by rewriting (1/e^2) as e^(-2).
2. Equate the exponents and set up the equation.
3. Simplify the equation by grouping like terms.
4. Solve for x by isolating it on one side.
5. Divide both sides by the coefficient of x to find the solution.
6. Simplify the solution if necessary.
I hope this helps! Let me know if you have any further questions.