What is the answer to 100=(300)/(1+e^{4-t)} ?

The answer to 100=(300)/(1+e^{4-t)} is t=-ln(2)+4

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100=(300)/(1+e^{4-t)}

100 = \frac{300}{1 + e ^{4 - t}}

t = - ln (2) + 4

Decimal Notation

t = 3.30685 \dots

Solution steps

100 = \frac{300}{1 + e ^{4 - t}}

Multiply both sides by

1 + e^{4 - t}

100 (1 + e^{4 - t}) = \frac{300}{1 + e ^{4 - t}} (1 + e^{4 - t})

Simplify

100 (1 + e^{4 - t}) = 300

Divide both sides by

100

1 + e^{4 - t} = 3

Move

1

to the right side

e^{4 - t} = 2

Apply exponent rules

4 - t = ln (2)

Solve

4 - t = ln (2) : t = - ln (2) + 4

t = - ln (2) + 4

Verify Solutions:

t = - ln (2) + 4

True

The solution is

t = - ln (2) + 4

8^{x} = 4^{x + 1}

6^{2 x - 6} = 3 6^{3 x - 5}

2^{x} - x^{2} = 0

(0.5)^{\frac{9900}{x}} = 0.3

5^{2 x + 1} = 6 (5^{x}) - 1

What is the answer to 100=(300)/(1+e^{4-t)} ?
The answer to 100=(300)/(1+e^{4-t)} is t=-ln(2)+4