What is the answer to (500)/(100-e^{x/2)}=20 ?

The answer to (500)/(100-e^{x/2)}=20 is x=2ln(75)

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(500)/(100-e^{x/2)}=20

\frac{500}{100 - e ^{\frac{x}{2}}} = 20

x = 2 ln (75)

Decimal Notation

x = 8.63497 \dots

Solution steps

\frac{500}{100 - e ^{\frac{x}{2}}} = 20

Multiply both sides by

100 - e^{\frac{x}{2}}

\frac{500}{100 - e ^{\frac{x}{2}}} (100 - e^{\frac{x}{2}}) = 20 (100 - e^{\frac{x}{2}})

Simplify

500 = 20 (100 - e^{\frac{x}{2}})

Switch sides

20 (100 - e^{\frac{x}{2}}) = 500

Divide both sides by

20

100 - e^{\frac{x}{2}} = 25

Move

100

to the right side

- e^{\frac{x}{2}} = - 75

Divide both sides by

- 1

e^{\frac{x}{2}} = 75

Apply exponent rules

\frac{x}{2} = ln (75)

Solve

\frac{x}{2} = ln (75) : x = 2 ln (75)

x = 2 ln (75)

Verify Solutions:

x = 2 ln (75)

True

The solution is

x = 2 ln (75)

7^{x + 2} = 5764801

3^{2 x} = 4^{(x + 1)}

15 = 17 e^{- (0.116) t}

2^{x + 1} + 2^{x - 2} = \frac{9}{2}

2^{x + 3} - 2^{x} = 112

What is the answer to (500)/(100-e^{x/2)}=20 ?
The answer to (500)/(100-e^{x/2)}=20 is x=2ln(75)