How do you solve -5e^(-x)+9=65ex+9=6?

1 Answer
Sep 6, 2016

x = - ln((3) / (5))x=ln(35)

Explanation:

We have: - 5 e^(- x) + 9 = 65ex+9=6

Let's begin by subtracting 99 from both sides of the equation:

=> - 5 e^(- x) = - 35ex=3

Then, let's divide both sides by - 55:

=> e^(- x) = (3) / (5)ex=35

Now, let's apply the natural logarithm to both sides:

=> ln(e^(- x)) = ln((3) / (5))ln(ex)=ln(35)

Using the laws of logarithms:

=> - x ln(e) = ln((3) / (5))xln(e)=ln(35)

=> - x cdot 1 = ln((3) / (5))x1=ln(35)

=> - x = ln((3) / (5))x=ln(35)

Finally, to solve for xx, let's divide both sides by - 11:

=> x = - ln((3) / (5))x=ln(35)