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

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

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

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

x = - ln (2) + 4

Decimal Notation

x = 3.30685 \dots

Solution steps

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

Multiply both sides by

1 + e^{4 - x}

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

Simplify

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

Divide both sides by

100

1 + e^{4 - x} = 3

Move

1

to the right side

e^{4 - x} = 2

Apply exponent rules

4 - x = ln (2)

Solve

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

x = - ln (2) + 4

Verify Solutions:

x = - ln (2) + 4

True

The solution is

x = - ln (2) + 4

2^{x + 5} 8 = 1 6^{2 x + 2}

2^{x + 3} = \frac{1}{32}

2 (1 6^{x}) - 5 (4^{x}) + 2 = 0

2^{x} + 4^{x} + \frac{1}{4} = 0

100 = 2^{x}

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