What is the answer to e^{x/(200)}+2e^{-x/(200)}=4 ?

The answer to e^{x/(200)}+2e^{-x/(200)}=4 is x=200ln(2+2^{1/2}),x=200ln(2-2^{1/2})

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e^{x/(200)}+2e^{-x/(200)}=4

e^{\frac{x}{200}} + 2 e^{- \frac{x}{200}} = 4

x = 200 ln (2 + 2^{\frac{1}{2}}), x = 200 ln (2 - 2^{\frac{1}{2}})

Decimal Notation

x = 245.58943 \dots, x = - 106.95999 \dots

Solution steps

e^{\frac{x}{200}} + 2 e^{- \frac{x}{200}} = 4

Apply exponent rules

(e^{x})^{0.005} + 2 (e^{x})^{- 0.005} = 4

Rewrite the equation with

e^{x} = u

(u)^{0.005} + 2 (u)^{- 0.005} = 4

Solve

u^{0.005} + 2 u^{- 0.005} = 4 : u = (2 + 2^{\frac{1}{2}})^{200}, u = (2 - 2^{\frac{1}{2}})^{200}

u = (2 + 2^{\frac{1}{2}})^{200}, u = (2 - 2^{\frac{1}{2}})^{200}

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = (2 + 2^{\frac{1}{2}})^{200} : x = 200 ln (2 + 2^{\frac{1}{2}})

Solve

e^{x} = (2 - 2^{\frac{1}{2}})^{200} : x = 200 ln (2 - 2^{\frac{1}{2}})

x = 200 ln (2 + 2^{\frac{1}{2}}), x = 200 ln (2 - 2^{\frac{1}{2}})

6^{x + 1} = 1 3^{x}

5^{x + 1} + 5^{x} + 5^{x - 1} = 31

2^{x + 2} + 5 \times 2^{x - 1} = \frac{13}{16}

4 e^{3 - x} = 3^{2 x + 5}

5^{n} = 125

What is the answer to e^{x/(200)}+2e^{-x/(200)}=4 ?
The answer to e^{x/(200)}+2e^{-x/(200)}=4 is x=200ln(2+2^{1/2}),x=200ln(2-2^{1/2})