5 divided by (3-e to the -x power)=4
5/(3- e^-x) = 4
5 = 12 - 4 e^-x
4 e^-x = 7
e^-x = 7/4
e^x = 4/7
Take natural logs of both sides,
x = ln (4/7) = -0.5596
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) ≈ -0.5596 (rounded to four decimal places).
Therefore, the value of x that satisfies the equation is approximately -0.5596.