## To solve the equation 5 divided by (3 minus e to the power of negative x) equals 4, we can follow these steps:

1. Start with the given equation: 5/(3 - e^(-x)) = 4.

2. Multiply both sides of the equation by (3 - e^(-x)) to eliminate the denominator on the left side:

5 = 4(3 - e^(-x)).

3. Distribute 4 into the parentheses:

5 = 12 - 4 e^(-x).

4. Move the constant term to the right side of the equation:

4 e^(-x) = 12 - 5.

5. Simplify:

4 e^(-x) = 7.

6. Divide both sides of the equation by 4 to isolate e^(-x):

e^(-x) = 7/4.

7. Take the natural logarithm of both sides to eliminate the exponential:

ln(e^(-x)) = ln(7/4).

8. Apply the logarithmic property to simplify the left side:

-x ln(e) = ln(7/4).

9. Since ln(e) is equal to 1, the equation becomes:

-x = ln(7/4).

10. Finally, divide both sides of the equation by -1 to solve for x:

x = -ln(7/4) â‰ˆ -0.5596 (rounded to four decimal places).

Therefore, the value of x that satisfies the equation is approximately -0.5596.