# Thread: Find n in an equation

1. ## Find n in an equation

Question 1:
A computer analysis shows that the number
n of electronic components a company should produce for supply to equal demand is found by solving the
equation

(n^2) /
500000 = 144 - (n/500)

Find
n.

Question 2:
Solve the equation ln 128 -
3 ln(x^2) = ln 2.

2. Originally Posted by fyremelody
Question 1:
A computer analysis shows that the number
n of electronic components a company should produce for supply to equal demand is found by solving the
equation

(n^2) /
500000 = 144 - (n/500)

Find
n.

Question 2:
Solve the equation ln 128 -
3 ln(x^2) = ln 2.
"/" is standard notation for division - x/500 is an acceptable way of saying "x divided by 500"

$\displaystyle n^2 = 5 \times 10^4 \left(144- \frac{n}{500}\right) = 7.2 \times 10^6 - 100n$

This is equal to $\displaystyle n^2 + 100n - 7.2 \times 10^6 = 0$ and since it's a quadratic use the ol' quadratic formula to solve

----------------------------

$\displaystyle 128 = 2^7$

Use the laws of logs to solve this one as well as the hint above

$\displaystyle \ln (2^7) - \ln (x^6) = \ln \left(\frac{2^7}{x^6}\right) = \left 2$

$\displaystyle \left(\frac{2^7}{x^6}\right) = 2$