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Popular >

4/(2-e^{-x)}=5

Solution

\frac{4}{2 - e ^{- x}} = 5

Solution

x = - ln (\frac{6}{5})

+1

Decimal Notation

x = - 0.18232 \dots

Solution steps

\frac{4}{2 - e ^{- x}} = 5

Multiply both sides by

2 - e^{- x}

\frac{4}{2 - e ^{- x}} (2 - e^{- x}) = 5 (2 - e^{- x})

Simplify

4 = 5 (2 - e^{- x})

Switch sides

5 (2 - e^{- x}) = 4

Divide both sides by

5

2 - e^{- x} = \frac{4}{5}

Move

2

to the right side

- e^{- x} = - \frac{6}{5}

Divide both sides by

- 1

e^{- x} = \frac{6}{5}

Apply exponent rules

- x = ln (\frac{6}{5})

Solve

- x = ln (\frac{6}{5}) : x = - ln (\frac{6}{5})

x = - ln (\frac{6}{5})

Verify Solutions:

x = - ln (\frac{6}{5})

True

The solution is

x = - ln (\frac{6}{5})

Popular Examples

9*3^{y-1}-3^y=18

9 \cdot 3^{y - 1} - 3^{y} = 18

36^{3x+4}=7776^{-2}

3 6^{3 x + 4} = 777 6^{- 2}

7^{x} - 7^{1 - x} = 6

sqrt(27^{x+2)}=729

2 7^{x + 2} = 729

1 = 2^{y}

Frequently Asked Questions (FAQ)

What is the answer to 4/(2-e^{-x)}=5 ?
The answer to 4/(2-e^{-x)}=5 is x=-ln(6/5)