What is the answer to 200=(500)/(1+e^{3-t)} ?

The answer to 200=(500)/(1+e^{3-t)} is t=-ln(3/2)+3

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200=(500)/(1+e^{3-t)}

200 = \frac{500}{1 + e ^{3 - t}}

t = - ln (\frac{3}{2}) + 3

Solution steps

200 = \frac{500}{1 + e ^{3 - t}}

Multiply both sides by

1 + e^{3 - t}

200 (1 + e^{3 - t}) = \frac{500}{1 + e ^{3 - t}} (1 + e^{3 - t})

Simplify

200 (1 + e^{3 - t}) = 500

Divide both sides by

200

1 + e^{3 - t} = \frac{5}{2}

Move

1

to the right side

e^{3 - t} = \frac{3}{2}

Apply exponent rules

3 - t = ln (\frac{3}{2})

Solve

3 - t = ln (\frac{3}{2}) : t = - ln (\frac{3}{2}) + 3

t = - ln (\frac{3}{2}) + 3

Verify Solutions:

t = - ln (\frac{3}{2}) + 3

True

The solution is

t = - ln (\frac{3}{2}) + 3

5^{2 x} + 5^{1 + x} - 6 = 0

4^{5 - 2 x} = 3^{x}

2 (1.08)^{x} = 2.5

200 = 4^{x}

8^{4 x} = \frac{1}{2 2}

What is the answer to 200=(500)/(1+e^{3-t)} ?
The answer to 200=(500)/(1+e^{3-t)} is t=-ln(3/2)+3