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Popular >

(100)/(1+e^{-x)}=2

Solution

\frac{100}{1 + e ^{- x}} = 2

Solution

x = - 2 ln (7)

+1

Decimal Notation

x = - 3.89182 \dots

Solution steps

\frac{100}{1 + e ^{- x}} = 2

Multiply both sides by

1 + e^{- x}

\frac{100}{1 + e ^{- x}} (1 + e^{- x}) = 2 (1 + e^{- x})

Simplify

100 = 2 (1 + e^{- x})

Switch sides

2 (1 + e^{- x}) = 100

Divide both sides by

2

1 + e^{- x} = 50

Move

1

to the right side

e^{- x} = 49

Apply exponent rules

- x = ln (49)

Solve

- x = ln (49) : x = - 2 ln (7)

x = - 2 ln (7)

Verify Solutions:

x = - 2 ln (7)

True

The solution is

x = - 2 ln (7)

Popular Examples

5*10^{x+2}=5000

5 \cdot 1 0^{x + 2} = 5000

(4^{x+1})/(2^{x+2)}=128

\frac{4 ^{x + 1}}{2 ^{x + 2}} = 128

9^{2 x - 1} = 2187

3 - e^{- 2 x} = 0

2=(1+(0.065)/(12))^t

2 = (1 + \frac{0.065}{12})^{t}

Frequently Asked Questions (FAQ)

What is the answer to (100)/(1+e^{-x)}=2 ?
The answer to (100)/(1+e^{-x)}=2 is x=-2ln(7)